Question

A string of length $2m$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500Hz$, then the waves would travel on it with a velocity of

• A. $125m{s}^{-1}$
• B. $250m{s}^{-1}$
• C. $500m{s}^{-1}$
• D. $1000m{s}^{-1}$

Answer 1

The correct option is C

$500m{s}^{-1}$

Step 1: Given that

Length of string, $L=2m$

Frequency of vibration, $f=500Hz$

Step 2: Find velocity of wave

For string $\lambda =2l/p$

Here, $p=$number of loops$=$order of vibration

Therefore, for the fourth mode $p=4$

$\Rightarrow \lambda =l/2$

Hence, velocity of wave, $v=f\lambda$

$=500\times (2/2)$

$=500m/s$

Hence, option (C) is correct.