Question

A sound wave travels at a speed of 339$m{{s}^{-1}}$. If its wavelength is 1.5 cm, what is the frequency of the wave? Will it be audible?

Answer 1

Hint: Every wave follows the relation where wave velocity is equal to the product of its frequency and wavelength. Also audible frequency range for the human ear is 20 Hz to 20 kHz. Any wave with frequency between this range can be intercepted by the human ear.

Complete Step By Step Solution:
Wavelength (represented by$\lambda$) of a wave is the distance travelled by it in one time period. Time period (represented by T) is the time taken to complete one cycle of compression and rarefaction. Wave speed (represented by v) is the speed of disturbance. So we can say that
$\lambda =vT$
Frequency is the number of waves per unit second. So
$T=\dfrac{1}{f}$
$v=f\lambda$
In the given question v=339$m{{s}^{-1}}$ and $\lambda$=1.5 cm or 0.015 m. So
$f=\dfrac{v}{\lambda }=\dfrac{339}{0.015}=22600$
Since the audible range for the human ear is 20 Hz to 20 kHz, this sound will not be audible.

Additional Information:
Sound waves travel fastest in solid because of compact packing of particles in solid. Every wave follows the above relation irrespective of being longitudinal, transverse, mechanical, non mechanical etc. Sound waves are longitudinal and mechanical waves. Sound waves travel with series of compression and rarefaction. Compressions are the region of high pressure whereas rarefactions are the region of low pressure.

Note: Always check the unit before putting values of quantities in formula. All the quantities must be in S.I. units. For example, in this question wavelength was given to us in centimeters, so before applying the formula it must be converted in meters. The audible frequency range for the human ear must be remembered as it can be used in question and will always be not provided.