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  4. 'n' number of waves are produced on a string in 0.5 second. Now the tension in the string is doubled (Assume length and radius constant), the number of waves produced in 0.5 second for the same harmonic will be)

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Q. 'n' number of waves are produced on a string in $0.5$ second. Now the tension in the string is doubled (Assume length and radius constant), the number of waves produced in $0.5$ second for the same harmonic will be)

MHT CETMHT CET 2018Waves

Solution:

For a stationary wave,
$n=\frac{1}{2 L} \sqrt{\frac{T}{m}} \,\,\,\,\,\,\,\,\, ....(i)$
where, $T=$ tension in string
$L=$ length of string
and $\,\,\,\,\, m=$ mass of string.
According to the question,
$n'=\frac{1}{2 L} \sqrt{\frac{T '}{m}} $
Here,$\,\,\,\,\,\,T' =2 T$
$n'=\frac{1}{2 L} \sqrt{\frac{2 T}{m}} \Rightarrow n'=\sqrt{2} \frac{1}{2 L} \sqrt{\frac{T}{m}}$
From Eq. (i), we get
$n'=\sqrt{2} n$