Question

A tuning fork of frequency $220Hz$ produces sound waves of wavelength $1.5m$ in air at $STP$. Calculate the increase in wavelength, (in metre) when temperature of air is $27^{\circ }C$

Answer 1

Answer: 0.07

Given $f=220Hz$,
${\lambda }_0=1.5m$ at $T_0=273K$
Speed of sound at STP, $v_0=f{\lambda }_0=220\times 1.5=330m/s$
Final temperature, $T=273+27=300K$
Let v the speed of sound at this temperature, then
$\frac{v}{v_0}=\sqrt{\frac{T}{T_0}}$
$\therefore v=v_0\sqrt{\frac{T}{T_0}}$
$=330\sqrt{\frac{300}{273}}=346.1m/s$
Final wavelength, $\lambda =\frac{v}{f}=\frac{346.1}{220}=1.57m$
The increase in wavelength $=\lambda -{\lambda }_0=1.57-1.50=0.07m$