Receiving Helpdesk

rarefaction wave definition

by Prof. Maximillia Kautzer Published 3 years ago Updated 2 years ago

Rarefaction is the reduction of an item's density, the opposite of compression. Like compression, which can travel in waves (sound waves, for instance), rarefaction waves also exist in nature. A common rarefaction wave is the area of low relative pressure following a shock wave (see picture).

Full Answer

What is rarefaction in sound waves?

This is the wave's crest, or peak. A rarefaction is the area of a wave (or Slinky) that is spread out. This is the wave's trough.

What is rarefaction and how does it work?

2 days ago · Rarefaction is a property of longitudinal waves. Explore the lesson, images, and examples to learn about rarefaction. Updated: 02/28/2022

What are rarefactions and compressions of a wave?

29/08/2021 · Rarefaction spreads through expansive and longitudinal waves that, over time, lengthen. The sound , for example, it is formed by the succession of numerous rarefaction and compression waves that propagate through the air.

Do rarefaction waves expand with time?

rarefaction wave. [ ¦rer·ə¦fak·shən ‚wāv] (fluid mechanics) A pressure wave or rush of air or water induced by rarefaction; it travels in the opposite direction to that of a shock wave directly following an explosion. Also known as suction wave.

What does Rarefraction mean in waves?

rarefaction, in the physics of sound, segment of one cycle of a longitudinal wave during its travel or motion, the other segment being compression. ... This is rarefaction. A succession of rarefactions and compressions makes up the longitudinal wave motion that emanates from an acoustic source.

What is rarefaction waves science?

A rarefaction is the area of a wave (or Slinky) that is spread out. This is the wave's trough. You can also think of a rarefaction in terms of density: The rarefaction is the part of the wave that has the lowest density.05-Jun-2016

What is rarefaction and compression?

Compression is that part of longitudinal wave in which the medium of particles are closer and there is momentary decrease in volume of medium. Rarefaction is that part of longitudinal wave in which the medium of particles apart and there is momentary increase in volume of medium. Physics.

Where is a rarefaction on a wave?

A rarefaction is a region in a longitudinal wave where the particles are furthest apart. As seen in Figure 9.2, there are regions where the medium is compressed and other regions where the medium is spread out in a longitudinal wave.

What is a rarefaction quizlet?

Rarefaction (definition) places where molecules of air are not squeezed and are spread out (opposite of compression)

How rarefaction is formed?

When a vibrating object goes forward in air as medium it pushes and compresses the air. This is the compression. When a vibrating object goes back in air as medium it creates a region of low pressure. This is the rarefaction.

What is rarefaction in physics class 9?

When a vibrating object moves backward in air as medium, it creates a region of low pressure. This region is called a rarefaction.15-May-2020

What is the difference between a compression and rarefaction in a sound wave?

Compressions and Rarefactions Because of the longitudinal motion of the air particles, there are regions in the air where the air particles are compressed together and other regions where the air particles are spread apart. These regions are known as compressions and rarefactions respectively.

What is compression and rarefaction Class 8?

Compressions: The particles are closest to each other in this. The density of the medium is maximum at compression. Rarefaction: The particles are farthest from each other. The density of the medium is minimum for rarefaction.

Why is it called a rarefaction?

Most of the time, rarefaction refers to air or other gases becoming less dense. When rarefaction occurs, the particles in a gas become more spread out. You may come across this word in the context of sound waves. A sound wave moving through air is made up of alternating areas of higher and lower density.

What is a rarefaction in a longitudinal wave?

Longitudinal waves show areas of compression and rarefaction : compressions are regions of high pressure due to particles being close together. rarefactions are regions of low pressure due to particles being spread further apart.

Is a rarefaction a trough?

low point is called the trough. For longitudinal waves, the compressions and rarefactions are analogous to the crests and troughs of transverse waves. The distance between successive crests or troughs is called the wavelength.

The longitudinal wave formula is given by the equation _____.

y(x,t)=y o cos[w(t-x/c)]

List the characteristics of sound?

The characteristics of the sound are as follows: Loudness Pitch Quality

What happens when a pebble is dropped into a pond with still water?

When a pebble is dropped into a pond with still water, there is the formation of ripples on the surface of the water. These ripples are in the circ...

State true or false: Mechanical waves are also known as elastic waves.

The given statement is true. Mechanical waves are also known as elastic waves because they depend on the elastic property of the waves.

Name the condition in which sound waves can travel through the gas.

For a sound wave to travel through the gas, the required condition is an adiabatic condition. This is because when the sound waves travel they prod...

What is rarefaction in science?

Definition of rarefaction. 1 : the action or process of rarefying. 2 : the quality or state of being rarefied. 3 : a state or region of minimum pressure in a medium traversed by compressional waves (such as sound waves) Other Words from rarefaction Example Sentences Learn More About rarefaction. Keep scrolling for more.

What does "rarefied" mean?

1 : the action or process of rarefying. 2 : the quality or state of being rarefied especially : an increase in porosity areas of rarefaction in the bones.

What is rarefaction in physics?

Rarefaction, in the physics of sound, segment of one cycle of a longitudinal wave during its travel or motion, the other segment being compression.

What happens when a tuning fork vibrates?

If the prong of a tuning fork vibrates in the air, for example, the layer of air adjacent to the prong undergoes compression when the prong moves so as to squeeze the air molecules together. When the prong springs back in the opposite direction, however, it leaves an area of reduced air pressure. This is rarefaction.

What is the distance between successive crests or troughs called?

The distance between successive crests or troughs is called the wavelength. The height of a wave is the amplitude. How many crests or troughs pass a specific point during a unit of time is…. compression. Compression, decrease in volume of any object or substance resulting from applied stress.

What is compression measured against?

In the latter, compression is measured against the system’s volume at the standard pressure to which an organism is subjected—e.g., the pressure of the…. History at your fingertips.

What is rarefied vapor flow?

The vapor flow in this condition is usually referred to as rarefied vapor flow. Because of the low density, the vapor in the rarefied state is somewhat different from the conventional continuum state. Also, the vapor density gradient is very large along the axial direction of the heat pipe.

What is the net change in air pressure?

pressure cycles back and forth. For a completely pure tone, the net change in air pressure is nil (assuming an average of whole numbers of cycles). For most musical sounds however, the waveshape that describes the pressure moment-by-moment is for periods ‘more in one direction than the other’, skewed or lopsided. This is called asymmetry. See Figures 1.2 and 1.3. In a well sealed room containing music, it would have the effect of very slightly varying the atmospheric pressure over periods of several seconds.

What is rarefaction in a sound wave?

Rarefaction is the reduction of an item's density, the opposite of compression.

Where does rarefaction occur?

Physical examples. A natural example of rarefaction occurs in the layers of Earth's atmosphere. Because the atmosphere has mass, most atmospheric matter is nearer to the Earth due to the Earth's gravitation. Therefore, air at higher layers of the atmosphere is less dense, or rarefied, relative to air at lower layers.

Is air at higher layers of the atmosphere less dense?

Therefore, air at higher layers of the atmosphere is less dense, or rarefied, relative to air at lower layers. Thus rarefaction can refer either to a reduction in density over space at a single point of time, or a reduction of density over time for one particular area.

What are the characteristics of a sound?

The characteristics of the sound are as follows: 1 Loudness 2 Pitch 3 Quality

What is mechanical wave?

In Physics, we define wave as an oscillation about a fixed point, that is accompanied by the transfer of energy. When the transfer of energy takes place through a medium due to oscillation, the resultant wave is termed as a mechanical wave.

Is sound a longitudinal wave?

A sound wave is an example of a longitudinal wave. Water waves are an example of a transverse wave. It is made of refractions and compressions. It is made of troughs and crests. This wave can be produced in any medium such as gas, liquid or solid. This wave can be produced in solid and liquid’s surface.

What is the displacement of a particle in a transverse wave?

In transverse waves, the displacement of the particle is perpendicular to the direction of propagation of the wave. In a longitudinal wave, the displacement of the particle is parallel to the direction of the wave propagation.

What is compression in a longitudinal wave?

A compression in a longitudinal wave is a region where the particles are the closest together while rarefaction in a longitudinal wave is a region where the particles are spread out.

What is an example of a sound wave?

An example of sound waves in a longitudinal direction is the tuning fork. In Sound waves, the amplitude of the wave is the difference between the maximum pressure caused by the wave and the pressure of the undisturbed air. The propagation speed of sound depends upon the type, composition of the medium, and temperature through which it propagates.

What is the maximum displacement of a particle from its rest point?

Amplitude is the maximum displacement of the particle from its rest point. In a longitudinal wave, the distance from the equilibrium position in the medium to compression or rarefaction is the amplitude.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version347msRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[06:28:51] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[06:28:51] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[06:28:51] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[06:28:51] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[06:28:51] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[06:28:51] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[06:28:51] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[06:28:51] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[06:28:51] LOG.warning: mt_rand(): Passing null to parameter #2 ($max) of type int is deprecated in ...
  • warninglog[06:28:51] LOG.warning: htmlspecialchars(): Passing null to parameter #1 ($string) of type string is...
  • warninglog[06:28:51] LOG.warning: htmlspecialchars(): Passing null to parameter #1 ($string) of type string is...
  • Booting (12.63ms)
  • Application (333ms)
  • 1 x Application (96.22%)
    333.49ms
    1 x Booting (3.65%)
    12.63ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed310ms
    • select * from `posts` where `published_at` <= '2025-06-11 06:28:51' and `slug` = 'rarefaction-wave-definition' and `posts`.`deleted_at` is null limit 1
      2.95ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-11 06:28:51
      • 1. rarefaction-wave-definition
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 32521 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      4.38msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 32521
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      670μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      420μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      490μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      300ms/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 45648 limit 1
      1.46msview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 45648
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        lcKHq5vm3LQCXswB9L0fY77CW3JMib8vSeED8jyw
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/rarefaction-wave-definition" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /rarefaction-wave-definition
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=d9440d329d5f337b.1749603520.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImpscCtzb1ozUWN1dUFVd0tLZ1VvUFE9PSIsInZhbHVlIjoiblJ6V2l5MUtCdnpHU2draEhOZ3gzWm94d2hXdlMzOExUMFdPS1h3L1EvNWtnYnNsUU5SNnV3UHBHQ2c5ZkY2Y3Q4QXdrY0pWbGhTSTVuamxTSld3RTRVU29USi9CNlhMZ2ptN1Zwb1dOUnRHSFBRMksvMlFQdUtBY3VvZ1U1VmYiLCJtYWMiOiIyZWQxM2IzOWE4NDZmNGNjMmQ3MzY2MTE0OTY5Yzk3ZTY2Y2NhZTU3Yjg4MTJjZDA4MGRjMTcwMWFmYzI3YjQ1IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6ImlMU1J4SG9wN1loYXN0ZWhJWDUxYXc9PSIsInZhbHVlIjoiN0M5UGFRR3hZbDkwWW9oMGYzSE1GZXhKUW9nNzBKcFg0QzZ1REZ3WnFUbEl6WVhWcThsWXV5YlJZSW1NMGpQdmpIbllsUGltbWxQVUxwNm9leHlkK0xxb09vQzBwWVdBSmVPZmMxYVdwaU5HUkI5eTE3WUE3S1VxemlaK2Z6QWciLCJtYWMiOiI4NmVhMzAyZTc3YzJmMTlmZjVlMGJhZDhiMDdlYmM4Yjc1YjQ0NGMxOWMyODAxMWFjMmM3ZDYyZGYzMzA0OTYzIiwidGFnIjoiIn0%3D_pk_id.64.7c30=d9440d329d5f337b.1749603520.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImpscCtzb1ozUWN1dUFVd0tLZ1VvUFE9PSIsInZhbHVlIjoiblJ6V2l5MUtCdnpHU2draEhOZ3gzW" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.179" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "94dd29989cb190cb-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.179, 172.69.59.86" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/rarefaction-wave-definition" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/rarefaction-wave-definition" "REMOTE_PORT" => "48608" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.69.59.86" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=d9440d329d5f337b.1749603520.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImpscCtzb1ozUWN1dUFVd0tLZ1VvUFE9PSIsInZhbHVlIjoiblJ6V2l5MUtCdnpHU2draEhOZ3gzWm94d2hXdlMzOExUMFdPS1h3L1EvNWtnYnNsUU5SNnV3UHBHQ2c5ZkY2Y3Q4QXdrY0pWbGhTSTVuamxTSld3RTRVU29USi9CNlhMZ2ptN1Zwb1dOUnRHSFBRMksvMlFQdUtBY3VvZ1U1VmYiLCJtYWMiOiIyZWQxM2IzOWE4NDZmNGNjMmQ3MzY2MTE0OTY5Yzk3ZTY2Y2NhZTU3Yjg4MTJjZDA4MGRjMTcwMWFmYzI3YjQ1IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6ImlMU1J4SG9wN1loYXN0ZWhJWDUxYXc9PSIsInZhbHVlIjoiN0M5UGFRR3hZbDkwWW9oMGYzSE1GZXhKUW9nNzBKcFg0QzZ1REZ3WnFUbEl6WVhWcThsWXV5YlJZSW1NMGpQdmpIbllsUGltbWxQVUxwNm9leHlkK0xxb09vQzBwWVdBSmVPZmMxYVdwaU5HUkI5eTE3WUE3S1VxemlaK2Z6QWciLCJtYWMiOiI4NmVhMzAyZTc3YzJmMTlmZjVlMGJhZDhiMDdlYmM4Yjc1YjQ0NGMxOWMyODAxMWFjMmM3ZDYyZGYzMzA0OTYzIiwidGFnIjoiIn0%3D_pk_id.64.7c30=d9440d329d5f337b.1749603520.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6ImpscCtzb1ozUWN1dUFVd0tLZ1VvUFE9PSIsInZhbHVlIjoiblJ6V2l5MUtCdnpHU2draEhOZ3gzW" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.179" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "94dd29989cb190cb-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.179, 172.69.59.86" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1749603531.6371 "REQUEST_TIME" => 1749603531 ]
        request_cookies
        0 of 0
        array:4 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "XSRF-TOKEN" => "lcKHq5vm3LQCXswB9L0fY77CW3JMib8vSeED8jyw" "askhelpdesk_session" => "Xoa7dmJfIYqbXykTsAlTr6aDHLqG13UFsOwZ0u8U" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Wed, 11 Jun 2025 00:58:51 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlVNZDRKOVNRVFp4Y24xMnNvQUFNS1E9PSIsInZhbHVlIjoiUEU3U3M1MWxMVlZ6Y2pqK3pUVjV1Z2JBeTVOdjBmN1dUY3ZvcHJoZXExTWc1d2JhenZkWUVlRnJmZFExbU8vMVBJOE1nKzZHU1lZUXF3OFN0STBGWlpNc2o3aG11Uk45Z2dOSXdhQWNVVERGdEh6bWJncGhtQkpNa0lhclRnVzkiLCJtYWMiOiJmOGZhYzk2NWY5MmE0YWFkMmZhNThkNGRmMTBlNjdjMWJiY2VjMjBkNDM2ZDVjYWUzOTEyODgyODA5Njg5OTcxIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 02:58:51 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IlVNZDRKOVNRVFp4Y24xMnNvQUFNS1E9PSIsInZhbHVlIjoiUEU3U3M1MWxMVlZ6Y2pqK3pUVjV1Z2JBeTVOdjBmN1dUY3ZvcHJoZXExTWc1d2JhenZkWUVlRnJmZFExbU8vMVBJOE1nK" 1 => "askhelpdesk_session=eyJpdiI6IlNsN2Mxa0wrWUE5bXZyYTF4Y2VId2c9PSIsInZhbHVlIjoiREhMa0F1M0JOSzJRUW9HWlR3Mk8vM3QxRHR0TnpmZW1uOGlsV2h6V09vcVFxcG1SSExjTFpoWFpLSWFKRGgwVVRvYzkzQjhiVVNOY3NUY0x4TlFHZDl0WllwcXllWWpFeEd2STVjbGlvcXIvVUNjcitvUGpTSTNyRWw3ME1WV3ciLCJtYWMiOiJjZmUwYWU4MmE3YmQ0NDljNGJkNGFjNDUzOWIzZGMwYWM4M2ViNDZhY2I5ODIzZmQ5ODNmZTczYzFkNTVlNTAyIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 02:58:51 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6IlNsN2Mxa0wrWUE5bXZyYTF4Y2VId2c9PSIsInZhbHVlIjoiREhMa0F1M0JOSzJRUW9HWlR3Mk8vM3QxRHR0TnpmZW1uOGlsV2h6V09vcVFxcG1SSExjTFpoWFpLSWFKRGgw" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IlVNZDRKOVNRVFp4Y24xMnNvQUFNS1E9PSIsInZhbHVlIjoiUEU3U3M1MWxMVlZ6Y2pqK3pUVjV1Z2JBeTVOdjBmN1dUY3ZvcHJoZXExTWc1d2JhenZkWUVlRnJmZFExbU8vMVBJOE1nKzZHU1lZUXF3OFN0STBGWlpNc2o3aG11Uk45Z2dOSXdhQWNVVERGdEh6bWJncGhtQkpNa0lhclRnVzkiLCJtYWMiOiJmOGZhYzk2NWY5MmE0YWFkMmZhNThkNGRmMTBlNjdjMWJiY2VjMjBkNDM2ZDVjYWUzOTEyODgyODA5Njg5OTcxIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 02:58:51 GMT; path=/XSRF-TOKEN=eyJpdiI6IlVNZDRKOVNRVFp4Y24xMnNvQUFNS1E9PSIsInZhbHVlIjoiUEU3U3M1MWxMVlZ6Y2pqK3pUVjV1Z2JBeTVOdjBmN1dUY3ZvcHJoZXExTWc1d2JhenZkWUVlRnJmZFExbU8vMVBJOE1nK" 1 => "askhelpdesk_session=eyJpdiI6IlNsN2Mxa0wrWUE5bXZyYTF4Y2VId2c9PSIsInZhbHVlIjoiREhMa0F1M0JOSzJRUW9HWlR3Mk8vM3QxRHR0TnpmZW1uOGlsV2h6V09vcVFxcG1SSExjTFpoWFpLSWFKRGgwVVRvYzkzQjhiVVNOY3NUY0x4TlFHZDl0WllwcXllWWpFeEd2STVjbGlvcXIvVUNjcitvUGpTSTNyRWw3ME1WV3ciLCJtYWMiOiJjZmUwYWU4MmE3YmQ0NDljNGJkNGFjNDUzOWIzZGMwYWM4M2ViNDZhY2I5ODIzZmQ5ODNmZTczYzFkNTVlNTAyIiwidGFnIjoiIn0%3D; expires=Wed, 11-Jun-2025 02:58:51 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6IlNsN2Mxa0wrWUE5bXZyYTF4Y2VId2c9PSIsInZhbHVlIjoiREhMa0F1M0JOSzJRUW9HWlR3Mk8vM3QxRHR0TnpmZW1uOGlsV2h6V09vcVFxcG1SSExjTFpoWFpLSWFKRGgw" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "lcKHq5vm3LQCXswB9L0fY77CW3JMib8vSeED8jyw" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/rarefaction-wave-definition" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]