Question

A bat can hear sound at frequencies up to 120 kHz. Determine the wavelength of sound in the air at this frequency. Take the speed of sound in the air as 344 m/s :

• A. $1.87\times {10}^{-3}m$
• B. $2.78\times {10}^{-3}m$
• C. $3.87\times {10}^{-3}m$
• D. $4.87\times {10}^{-3}m$

Answer 1

The correct option is B $2.78\times {10}^{-3}m$

The relationship between the frequency, wavelength and speed of sound or velocity is given as follows.
$Frequency\nu =\frac{wavevelocityv}{wavelength\lambda }$
From the above equation, wavelength is derived as, $Wavelength\lambda =\frac{wavevelocityv}{Frequency\nu }$

In the question, the velocity of sound is 344 m/s and frequency=120 kHz = $120\times {10}^{3}Hz$ is given.
Therefore,
$Wavelength\lambda =\frac{v}{\nu }=\frac{334m/s}{120\times {10}^{3}Hz}=2.87\times {10}^{-3}m$.

Hence, the wavelength of the sound wave is given as $2.87\times {10}^{-3}m$.