Question

A sonometer wire 100cm in length has a fundamental frequency of 330Hz. The velocity of propagation of transverse waves along this wire is:
A. $330m{{s}^{-1}}$
B. $660m{{s}^{-1}}$
C. $115m{{s}^{-1}}$
D.$990m{{s}^{-1}}$

Answer 1

As a very first step, you could read the question properly and hence write down the given values from the question. You could then recall the standard equation used for the fundamental frequency and then rewrite it in terms of velocity. Then you could simply substitute the given quantities to get the answer.

Formula Used
Fundamental frequency,
$\nu =\dfrac{n}{2L}\sqrt{\dfrac{T}{\mu }}$

Complete step-by-step solution:
In the question, we are given a sonometer wire of length 100cm with a fundamental frequency of 330Hz. We are supposed to find the velocity of propagation of transverse waves along this wire.
So, length ‘L’ of the sonometer wire is given as,
L=100cm=1m ………………………………… (1)
Now, we know that fundamental frequency of a sonometer wire could be given by the following formula,
$\nu =\dfrac{n}{2L}\sqrt{\dfrac{T}{\mu }}$ …………………………………. (2)
But we know that velocity of the transverse wave in the wire could be given by,
$V=\sqrt{\dfrac{T}{\mu }}$ …………………………………. (3)
From (2) and (3) we have,
$\nu =\dfrac{1}{2L}V$
Substituting the value of length ‘L’ from (1) we hget,
$\nu =\dfrac{1}{2\times 1}V$
But we are given the fundamental frequency to be 330Hz, so the velocity would be,
$V=2\times 330=660m{{s}^{-1}}$
Therefore, we found the velocity of propagation of transverse waves along the given sonometer wire to be$660m{{s}^{-1}}$. Option B is the correct answer.

Note: In the question, we are given the length of the sonometer wire in centimeters and we have converted this to meters. This is done because we are given all the other quantities along with the options in their respective SI units. So, we will have to convert the length in its SI unit.