Need help with a physics problem about wave functions

timer Asked: Nov 24th, 2015
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Question Description

A standing-wave pattern is observed in a thin wire with a length of 3.00 m. The wave function is y = 0.00200 sin(πx) cos(100πt) where x and y are in meters and t in seconds. 

(a) How many loops does this patten exhibit? (b) What is the fundamental frequency of vibration of the wire?

Tutor Answer

School: Duke University

Thank you for the opportunity to help you with your question!

The general wave function of a standing wave in a wire is:

y = 2A sin(kx) cos(ωt) comparing this general function with the given function we get:

k = π =2πλ or λ = 2.00 m and ω = 100π = 2πf or f = 50.0 Hz

(a) The distance between adjacent nodes dNN = λ/2 and the number of loops N on the wire

with length L = 3.00 m is:

N =L/dNN=2L/λ=(2 × 3.00)/2.00

(b) the speed of the wave in the wire is:

v = fλ = 50.0 × 2.00 = 100 m/s

The wavelength is:

λ = 2L = 6.00 m

This wave travels the wire with the same speed as the wave that fits 3 loops in the length

of the wire, so fundamental frequency is then:

f =vλ=(100 m/s)/6.00 m

= 16.7 Hz

Please let me know if you need any clarification. I'm always happy to answer your questions.

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