Question

A standing wave is produced in a $10\text{m}$ long string fixed at one end and free at the other end. Find the wavelength of wave, if string is vibrating in its second overtone, and wave velocity is $20\text{m/s}$.

• A. $5\text{m}$
• B. $4\text{m}$
• C. $10\text{m}$
• D. $8\text{m}$

Answer 1

The correct option is D $8\text{m}$

For second overtone $(n=2)$
$\Rightarrow f_5=(n+\frac{1}{2})\frac{V}{2L}=\frac{5V}{4L}$
$\Rightarrow f_2=\frac{5\times 20}{4\times 10}=2.5\text{Hz}$
Since velocity, $V=f\lambda$
$\Rightarrow \lambda =\frac{V}{f}=\frac{20}{2.5}=8\text{m}$

OR

For nth overtone
$\lambda =\frac{2L}{n+\frac{1}{2}}$
for second overtone,
$\lambda =\frac{4L}{5}=8\text{m}$