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. $125m/s$
• B. $250m/s$
• C. $500m/s$
• D. $1000m/s$

Answer 1

The correct option is C $500m/s$

Given, length of the string $l=2m$, frequency $n=500Hz$
For string
$\lambda =\frac{2l}{p}$
Where $p=$ number of loops $=$ order of vibration
Hence, for forth mode $p=4$
$\lambda =\frac{l}{2}$
Hence,
$v=n\lambda =500\times \frac{2}{2}=500m/s$
Final answer: $\left(c\right)$