Question

When the wavelength of sound changes from $1m$ to $1.01m$, the number of beats heard are $4$. The velocity of sound is

• A. $404m/s$
• B. $4.04m/s$
• C. $414m/s$
• D. $400m/s$

Answer 1

The correct option is A $404m/s$

Given : $b=4$ ${\lambda }_1=1m$ ${\lambda }_2=1.01m$

Number of beats $b={\nu }_1-{\nu }_2=v(\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2})$ where $\nu =\frac{v}{\lambda }$

$\therefore$ $4=v(\frac{1}{1}-\frac{1}{1.01})$ $⟹v=404$ $m/s$