Question

Velocity of sound in air is 340 m/s. A vibrating body produces sound waves of wavelength 0.01m that reach your ear through air. Will you be able to hear the sound? Justify your answer.

Answer 1

Velocity of a wave is given by where is the frequency of the wave and is the wavelength of the wave. Normal human ears are able to detect sounds in a frequency range from about 20 Hz to 20 kHz.

Complete step-by-step solution:
As given in the question that velocity of sound in air . Sound waves of wavelength from a vibrating body reach your ear through air.
We know that velocity of a wave is given by where is the frequency of the wave and is the wavelength of the wave.So, the frequency of sound wave is given by $v=\dfrac{v}{\lambda}$

Substituting the values of velocity and wavelength we have
$v=\dfrac{340}{0.01}=34000Hz$

We know that normal human ears are able to detect sounds of frequency range from about 20 Hz to 20 kHz. As 34000Hz is not in the audible range for humans, so, you will not be able to hear the sound.

Note:- Frequency is that the variety of occurrences of a continuance event per unit of your time. It is additionally observed as temporal frequency that emphasizes the distinction to spatial frequency and angular frequency. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a continuance event per second.
A normal human ear can detect sounds in a frequency range from about 20 Hz to 20000Hz. (A human child can actually detect sound frequencies slightly higher than 20 kHz, but lose some high-frequency sensitivity as they grow; the upper limit in average adults is mostly close to 15–17 kHz.) Most of the small mammals are sensitive to very high frequencies, but not to the lower frequencies. For example, some species of bats can detect sound of frequency as high as 200 kHz, but their lower limit is around 20 kHz which is the upper limit for young humans having normal hearing.