Question

A string vibrates in 4 segments to a frequency of 400 Hz. Its fundamental frequency is :

• A. $400Hz$
• B. $200Hz$
• C. $100Hz$
• D. $50Hz$

Answer 1

Answer: (C)

$100Hz$

Frequency of oscillation of string in $n^{th}$ harmonic is $\frac{nc}{2l}$.

where $c$ is the speed of the wave in the string.

Since the string vibrates in 4 segments, $n=4$

$400=\frac{4c}{2l}$

$⟹\frac{c}{2l}=100$

Fundamental frequency $f_1=\frac{1\times c}{2l}=100Hz$