Q:- A string of length 'l' is fixed at both ends.It is vibrating in its 3^rd overtone with maximum amplitude 'a'.The amplitude at a distance l/3 from one end is:

A. a

B. 0

C. (√3/2)a

D.a/2

Dear Tapasranjan It is vibrating in its 3rd overtone then you will get nodes at x=0 ,l/4,2l/4,3l/4,l equation of motion is y= a sin(4?x/l)coswt put x=l/3 amplitude =a sin(4?l/3l) =a sin(4?/3) =a(v3/2) Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation. All the best. Regards, Askiitians Experts Badiuddin

Dear Student,
Please find below the solution to your problem.

It is vibrating in its 3rd overtone
then you will get nodes at x=0 ,l/4,2l/4,3l/4,l
equation of motion is
y= a sin(4?x/l)coswt
put x=l/3
amplitude =a sin(4?l/3l)
=a sin(4?/3) =a(v3/2)

Thanks and Regards