Question

'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)

• A. n
• B. $\sqrt{2}$ n
• C. $\frac{n}{\sqrt{2}}$
• D. $\frac{n}{\sqrt{5}}$

Answer 1

Answer: (B)

For a stationary wave,
$n=\frac{1}{2L}\sqrt{\frac{T}{m}}....(i)$
where, $T=$ tension in string
$L=$ length of string
and $m=$ mass of string.
According to the question,
$n^{\prime }=\frac{1}{2L}\sqrt{\frac{T^{\prime }}{m}}$
Here,$T^{\prime }=2T$
$n^{\prime }=\frac{1}{2L}\sqrt{\frac{2T}{m}}\Rightarrow n^{\prime }=\sqrt{2}\frac{1}{2L}\sqrt{\frac{T}{m}}$
From Eq. (i), we get
$n^{\prime }=\sqrt{2}n$