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Solved: The wave function of a standing wave is y(x, t) =
Chapter 15, Problem 44E(choose chapter or problem)
Problem 44E
The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32.5 rad/m)x] sin [(754 rad/s)t]. For the two traveling waves that make up this standing wave, find the (a) amplitude; (b) wavelength; (c) frequency; (d) wave speed; (e) wave functions. (f) From the information given, can you determine which harmonic this is? Explain.
Questions & Answers
QUESTION:
Problem 44E
The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32.5 rad/m)x] sin [(754 rad/s)t]. For the two traveling waves that make up this standing wave, find the (a) amplitude; (b) wavelength; (c) frequency; (d) wave speed; (e) wave functions. (f) From the information given, can you determine which harmonic this is? Explain.
ANSWER:Solution 44E
Step 1:
The standard equation for the standing wave,
Where, A - Amplitude of the wave
k - Wave vector
x -displacement for the wave
- Angular velocity of the wave
t - Time
The wave vector, k = 2𝜋 / 𝜆
Where, 𝜆 - Wavelength of the wave
The angular velocity of the wave, = 2𝜋f
Where, f - frequency of the wave