Question

A string vibrates in 4 segments to a frequency of 400 Hz. What frequency will cause it to vibrate into 7 segments ?

• A. $700Hz$
• B. $500Hz$
• C. $400Hz$
• D. $100Hz$

Answer 1

The correct option is A $700Hz$

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, $n=4$

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

$⟹\frac{c}{2l}=100$

When string vibrates in 7 segments, $n=7$

Thus $f_7=\frac{7c}{2l}=700Hz$