Question

A $50\text{cm}$ string fixed at both ends produces resonant frequency $384\text{Hz}$ and $288\text{Hz}$ without there being any other resonant frequency between the two. Find the speed of the wave on the string in $\text{cm/sec}$.

Answer 1

Given :
$f_1=384\text{Hz}$
$f_2=288\text{Hz}$
$l=50\text{cm}$
change in a frequency, $\Delta f=f_1-f_2$
$\Delta f=384-288=96\text{Hz}$
The fundamental frequency is $f_0=96\text{Hz}$
$\lambda =2l=2\times 0.50=1\text{m}$
wave speed of the string will be
$v=f_0\lambda =96\times 1=96\text{m/s}$
$v=9600\text{cm/sec}$