Question

A string vibrates in $5$ segments to a frequency of $480\text{Hz}$. The frequency that will cause it to vibrate in $2$ segments will be

• A. $96\text{Hz}$
• B. $192\text{Hz}$
• C. $1200\text{Hz}$
• D. $2400\text{Hz}$

Answer 1

The correct option is B $192\text{Hz}$

As string is vibrating in full segments (loop), then string is fixed at both ends.

Frequency of vibrations is given by

$f=\frac{nv}{2l}$

For same string, $f\propto n$

So, $\frac{f_1}{f_2}=\frac{n_1}{n_2}$

$\Rightarrow \frac{480}{f_2}=\frac{5}{2}[1\text{segment}=1\text{loop}]$

$\Rightarrow f_2=192\text{Hz}$

So, option $\left(b\right)$ is correct.