Question

Stationary waves are produced in a $10\text{m}$ long stretched string. If the string vibrates in 5 segments and wave velocity is $20\text{m/sec}$, then the frequency is (in $\text{Hz}$)

Answer 1

Given that,
Lenght of the string, $L=10\text{m}$
Number of segments, $n=5$


So, $L=\frac{n\lambda }{2}$
$\Rightarrow L=\frac{5\lambda }{2}$
$\Rightarrow \lambda =\frac{2L}{5}$

Frequency $f=\frac{v}{\lambda }$
$\Rightarrow f=\frac{v}{\frac{2L}{5}}$
$\Rightarrow f=\frac{20\text{m/s}}{\frac{2\times 10\text{m}}{5}}=5\text{Hz}$