Question

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

Answer 1

Given $f =220\,Hz$,
$\lambda_{0} = 1.5 \,m$ at $T_{0} = 273\,K$
Speed of sound at STP, $v_{0} = f \lambda_{0} = 220 \times 1.5 = 330\, m/s$
Final temperature, $T=273+27 = 300\,K$
Let v the speed of sound at this temperature, then
$\frac{v}{v_{0}} = \sqrt{\frac{T}{T_{0}}} $
$\therefore v=v_{0} \sqrt{\frac{T}{T_{0}}}$
$=330\sqrt{\frac{300}{273}}=346.1 m/ s$
Final wavelength, $\lambda = \frac{v}{f}=\frac{346.1}{220}=1.57 \,m $
The increase in wavelength $=\lambda-\lambda_{0}=1.57-1.50=0.07\,m$