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Unit 6

6.3 Periodic Waves

3 min readnovember 3, 2020

Saarah Hasan

caroline49234295

Caroline Koffke


AP Physics 2 🧲

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6.3: Periodic Waves

First off, what even is a periodic wave? Don’t panic, it’s not too complicated!
A periodic wave is a wave that has a repeating continuous pattern; it’s essentially a wave that repeats for several cycles. It can be characterized by its wavelength, period, frequency, and amplitude. All the waves below can be considered periodic waves.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-tT5omHVA0rSy.png?alt=media&token=ee45fd6e-1ee2-4072-8c4f-559280d0f84a

Taken from Wikimedia Commons

The Wave Equation:

In Physics 2, we mainly focus on simple periodic waves that can be described with equations involving a sine or cosine function, as well as the wavelength, amplitude, and frequency of the wave.
As a function of time, the equation would look like:
f(t)=A cos(ω*t) ⏩ ω=2 π/Tω=2 π/T
F(t)=Acos(2π/T*t) ⏩ T=1/fT=1/f
F(t)=Acos(2π*f*t)
As a function of position, the equation would look like:
F(x)=A cos (2π/λ*x)
where
A=Amplitude
T=Period
f=Frequency
λ=Wavelength
t=Time
x=Position
ω= Angular Frequency
Let's practice together a little.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-uk4xoUYnUi2u.png?alt=media&token=9912ad79-9351-40ce-b0a2-a73c2245be44
Take a look at this graph, where the x-axis is the horizontal position and the y-axis is the vertical height of the wave.
What's the general equation for periodic waves that are graphed as a function of position?
F(x)=A cos (2π/λ*x)
What's the amplitude for this wave?
What's highest/lowest point on the graph? 4
What's the wavelength? (Measure the distance from crest to crest, or trough to trough)
(6-3)=3
And that's it! The equation for this wave would look like:
F(x)=A cos (2π/λ*x) ➡️ F(x)=4cos(2π/3*x)

Practice Problems:🧩

1.The frequency of the tuning fork is (approximately)
A) 0.0039 s
B) 0.020 s
C) 2.55 Hz
D) 50 Hz
E) 256 Hz
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ctIi6GWJhKSg.png?alt=media&token=59950cef-573f-44d8-a532-556cd706e092
2. What is the amplitude of the wave?
(A) 4 cm
(B) 5 cm
(C) 8 cm
(D) 10 cm
(E) 16 cm
3. What is the speed of the wave?
(A) 4 cm/s
(B) 25 cm/s
(C) 50 cm/s
(D) 100 cm/s
(E) 200 cm/s
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-dKLAzzwfSKZh.png?alt=media&token=71f1b714-0cb5-428b-9638-c3e0dad2e528
4. What is the length of the longest wavelength shown?
A) 0.5 m
B) 0.75 m
C) 1 m
D) 2 m
E) 4 m
5. Which organ pipe(s) shows a standing wave which has twice the frequency of one of the other waves shown?
A) Cy
B) Cz
C) Ox
D) Oy
E) Cy , Cz, Ox, Oy

Answers:
  1. E: f = cycles / seconds
  2. A: By inspection
  3. C: By inspection, the λ is 10 cm. f = 1 / T = 5, Then use v = f λ.
  4. E: Cx is only ¼ of a wavelength. To make a full wavelength you would need 4x the current length
  5. D: Wavelengths of each are (dist/cycle) … 4L, 4/3 L, 4/5 L, L, 2/3 L … Frequencies are f = v/ λ. v/4L, 3v/4L, 5v/4L, v/L, 3v/2L … Oy is 2x Cy

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