The equation for the vibration of a string fixed at both ends, vibrating in its its third harmonic is given by `y=0.4"sin" (pix)/(10) cos 600 pi t` where x and y are in cm
(1) What is the frequency of vibration ? (2) What are the positions of nodes?
(3) What is the length of string?
(4) What is the wavelength and speed of transverse waves that can interfer to give this vibration ?

Explanation

Comparing with `y=2a sin kx cos omega t` we have
(1) `omega=60 pi` gives `f=300 Hz`
(2) To get the position of nodes `"sin" (pix)/(10)=0`
i.,e `(pix)/(10)= n pi` where `n=0,1,2`....
Hence nodesoccur at x,0,10,20 cm.....
(3) since the string is in `3^(rd)` harmonic
`l=3(lambda)/(2)` gives `l=30 cm`
(4) Speed of wae `v=f lambda=300xx20=60 ms^(-1)`