Question

A $75cm$ string fixed at both ends produces resonant frequencies of $384Hz$ and $288Hz$ without there being any other resonant frequency between these two. Wave speed for the string is :

• A. $144m/s$
• B. $216m/s$
• C. $108m/s$
• D. $72m/s$

Answer 1

The correct option is A $144m/s$

Given,

$f_1=384Hz$

$f_2=288Hz$

$l=75cm$

Change in frequency, $\Delta f=f_1-f_2$

$\Delta f=384-288$

$\Delta f=96\times 4-96\times 3=96Hz$

The fundamental frequency is $f_0=96Hz$

We know that for fundamental frequency the distance between two consecutive nodes i.e. two points where the string is connected (in this case) is equal to half of wavelength

So, $\frac{\lambda }{2}=0.75$

$\lambda =2\times 0.75=1.5m$

Wave speed of the string will be

$v=f_0\lambda =96\times 1.5=144m/s$

The correct option is A.