Question

$n$ waves are produced on a string in one second. When the radius of the string is doubled and the tension is maintained the same, the number of waves produced in one second for the same harmonic will be

• A. $2n$
• B. $\frac{n}{3}$
• C. $\frac{n}{2}$
• D. $\frac{n}{\sqrt{2}}$

Answer 1

Answer: (D)

Given that the frequency of the wave produced in the string is $\frac{1}{n}$
$\therefore \frac{1}{n}=\frac{1}{2\pi }\sqrt{\frac{T}{m}}$
Now, $T^{\prime }=2T$
$\therefore$ New frequency is,
$f=\frac{1}{2\pi }\sqrt{\frac{2T}{m}}=\sqrt{2}\times \frac{1}{n}$
$\therefore$ Number of waves produced per second is,
$\frac{1}{f}=\frac{n}{\sqrt{2}}$