Need help with a physics problem about wave functions

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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?

Nov 24th, 2015

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.
Nov 24th, 2015

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