A stringed instrument generates a complex waveform with the followi...

Question
A stringed instrument generates a complex waveform with the following components:

250 Hz with an amplitude of 5

500 Hz with an amplitude of 3

750 Hz with an amplitude of 1

What is the fundamental frequency?

What other harmonics are represented?

What would be the equation for this waveform? (HINT: the equation only tells us the relationship between the harmonics, and not the actual frequencies represented.)

Calculate the amplitude values every 10 degrees and graph the waveform. You are welcome to do this in a spreadsheet if you know how.
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      • creating: site.layouts.app (581μs)
      • composing: site.layouts.app (23μs)
      • creating: components.canonical (540μs)
      • composing: components.canonical (105μs)
      • creating: components.open-graph (324μs)
      • composing: components.open-graph (94μs)
      • creating: site.headers.header (380μs)
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      • Illuminate\Cache\Events\CacheHit (3.28ms)
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      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheHit (531μs)
      • Illuminate\Cache\Events\CacheHit (2.2ms)
      • Illuminate\Cache\Events\CacheHit (304μs)
      • Illuminate\Cache\Events\CacheHit (467μs)
      • Illuminate\Cache\Events\CacheHit (437μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • creating: components.forms.contact-us (966μs)
      • composing: components.forms.contact-us (185μs)
      • creating: components.forms.get-started (168μs)
      • composing: components.forms.get-started (146μs)
      • creating: components.forms.free-tool-download (297μs)
      • composing: components.forms.free-tool-download (149μs)
      • creating: components.forms.claim-free-worksheet (188μs)
      • composing: components.forms.claim-free-worksheet (241μs)
      • creating: components.forms.tutor-subscription-waitlist (560μs)
      • composing: components.forms.tutor-subscription-waitlist (82μs)
      • creating: components.forms.tutor-subscription-join (426μs)
      • composing: components.forms.tutor-subscription-join (84μs)
      • creating: components.forms.tutor-support (124μs)
      • composing: components.forms.tutor-support (166μs)
      • 315 x Illuminate\Cache\Events\CacheHit (22.31%)
        190ms
        16 x Illuminate\Database\Events\StatementPrepared (6.65%)
        56.54ms
        16 x Illuminate\Database\Events\QueryExecuted (6.43%)
        54.65ms
        7 x Illuminate\Cache\Events\CacheMissed (2.26%)
        19.20ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (2.07%)
        17.56ms
        7 x Illuminate\Cache\Events\KeyWritten (0.88%)
        7.52ms
        1 x Illuminate\Routing\Events\Routing (0.19%)
        1.59ms
        8 x eloquent.retrieved: App\Models\SubjectCat (0.13%)
        1.13ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.13%)
        1.07ms
        1 x creating: components.forms.contact-us (0.11%)
        966μs
        1 x Illuminate\Routing\Events\RouteMatched (0.07%)
        581μs
        1 x creating: site.layouts.app (0.07%)
        581μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.07%)
        560μs
        1 x creating: components.canonical (0.06%)
        540μs
        1 x creating: components.breadcrumbs (0.06%)
        534μs
        1 x eloquent.booted: App\Models\Subject (0.05%)
        454μs
        1 x creating: components.forms.tutor-subscription-join (0.05%)
        426μs
        1 x creating: homework.show (0.05%)
        409μs
        1 x eloquent.booting: App\Models\SubjectCat (0.05%)
        405μs
        1 x creating: site.headers.header (0.04%)
        380μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        361μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        359μs
        1 x creating: components.open-graph (0.04%)
        324μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        306μs
        1 x creating: components.forms.free-tool-download (0.03%)
        297μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        284μs
        1 x composing: components.forms.claim-free-worksheet (0.03%)
        241μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        227μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        225μs
        1 x composing: components.breadcrumbs (0.02%)
        199μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        188μs
        1 x composing: components.forms.contact-us (0.02%)
        185μs
        1 x composing: homework.show (0.02%)
        178μs
        1 x creating: components.forms.get-started (0.02%)
        168μs
        1 x composing: components.forms.tutor-support (0.02%)
        166μs
        1 x composing: components.forms.free-tool-download (0.02%)
        149μs
        1 x composing: components.forms.get-started (0.02%)
        146μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        126μs
        1 x creating: components.forms.tutor-support (0.01%)
        124μs
        1 x composing: components.canonical (0.01%)
        105μs
        1 x composing: components.open-graph (0.01%)
        94μs
        1 x composing: components.footer (0.01%)
        92μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        84μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        82μs
        1 x composing: site.headers.header (0.01%)
        81μs
        1 x creating: components.footer (0.01%)
        77μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        66μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        60μs
        1 x composing: site.layouts.app (0%)
        23μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      16 statements were executed, 4 of which were duplicates, 12 unique. Show only duplicated79.49ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '20999' limit 1
        14.49mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 20999
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (268)
        950μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (20999)
        9.49mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        910μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 20999 and `subject` = 268 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        13.24mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 20999
        • 1: 268
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (268)
        1.01mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 20999 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        870μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20999
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 20999 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        2.81mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20999
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 20999 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        7.01mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20999
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        7.09mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        5.4mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        2.48mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.25mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        3.87mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        7.61mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\SubjectCat
      8SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          kpu078xtMUyybOmZAmYl0gskXLHaXxRrwRxziokF
          utm_source
          direct
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          /college-homework-library/Physics/Physics-Other/20999
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Physics/Physics...
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          PHPDEBUGBAR_STACK_DATA
          []
          path_info
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          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
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          request_cookies
          []
          
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