Question

Standing wave is produced in $10\text{m}$ long stretched string. If the string vibrates in $5$ segments and wave velocity is $20\text{m/s}$, then frequency of oscillation is

• A. $5\text{Hz}$
• B. $2\text{Hz}$
• C. $8\text{Hz}$
• D. $7\text{Hz}$

Answer 1

The correct option is A $5\text{Hz}$

Given, string is vibrating in $5$ segments.

We know that length of $1$ loop or segment is equal to $\frac{\lambda }{2}$.
$\Rightarrow L=5\times \left(\frac{\lambda }{2}\right)$
$\Rightarrow 10=\frac{5\lambda }{2}$
$\Rightarrow \lambda =4\text{m}$
So, $f=\frac{v}{\lambda }=\frac{20}{4}=5\text{Hz}$