Vibrations of a Stretched String: Finding Harmonic, Frequency & Wave Speed

[Fusilli_Jerry89]

Homework Statement

A 7 metre long string is stretched between 2 walls so that its ends are fixed. It is made to vibrate and it is found that the displacement, y is given by: y = 0.023sin(xpi)cos(0.714 pi t) where x and y are in metres and t is in milliseconds.

a) to which harmonic, N, does the vibrtion correspond?
b) What is the frequency of the sound emitted by the string?
c) What is the speed of waves in the string?

Homework Equations

y(N) = 2y sin((Npix)/L)cos((vNtpi)/L)

The Attempt at a Solution

To get part a, can u use the formula and see that L must equal N in order to get the equation in the question, or no? I'm lost.

 

[learningphysics]

Yes, you're right. N must equal L to get the equation you have:

y(N) = 2y sin((Npix)/L)cos((vNtpi)/L)

y = 0.023sin(xpi)cos(0.714 pi t)

So N = 7.

Another way to look at it... Find the angle at the end of the standing wave... The angle is xpi... that's coming from 0.023sin(xpi)cos(0.714 pi t)

So what's the angle you get when you plug in x = 7 (end of the standing wave since the walls are 7m apart). you get 7pi. That means the 7th harmonic.

Solve b using "0.714 pi t"

You should be able to solve c, in the same way as a... by comparing: y = 0.023sin(xpi)cos(0.714 pi t) to y(N) = 2y sin((Npix)/L)cos((vNtpi)/L)

what does v need to be...