A sound wave propagating in air has a frequency of 4000 Hz. Calculate the percentage change in wavelength…
A sound wave propagating in air has a frequency of 4000 Hz. Calculate the percentage change in wavelength when the wavefront initially in a region, where T = 27°C, enters a region, where the temperature decreases to 10°C.
Solution
Sol. $\dfrac{v_2}{v_1}=\sqrt{\dfrac{T_2}{T_1}}=\sqrt{\dfrac{273+10}{273+27}}=\sqrt{\dfrac{283}{300}}=0.97$
As, frequency remains unchanged, so
$\dfrac{v_2}{v_1}=\dfrac{v\lambda_2}{v\lambda_1}=\dfrac{\lambda_2}{\lambda_1}=0.97\quad(\therefore v=v\lambda)$
Percentage change in wavelength,
$\dfrac{\lambda_1-\lambda_2}{\lambda_1}\times100=\left(1-\dfrac{\lambda_2}{\lambda_1}\right)\times100=(1-0.97)\times100=3\%$
Answer: 3%