Question

Establish the relationship between speed of sound, its wavelength and frequency. If speed of sound in air is 340 $ms^{-1}$, calculate wavelength when frequency is 256 Hz :
A. 1 m
B. 2.5 m
C. 1.33 m
D. 3.45 m

Answer 1

Hint: Sound wave is a longitudinal wave. It propagates because the motion of particles of the medium oscillates about their mean position and passes their energies to the adjoining particles.

Formula used:
If the frequency of any wave in a medium is $\nu$ and its wavelength is $\lambda$, then its velocity is:
$velocity = \nu \lambda$.

Complete answer:
To establish a relation between frequency, wavelength and velocity of a wave we need to consider the definitions first. Frequency in case of sound waves, is the number of oscillations that a particle can complete in 1s. Wavelength is the distance between two successive compressions (or rarefactions).
We know that velocity is distance by time and in our case, frequency is inverse of time period. So multiplying wavelength and frequency will give us the velocity of the sound wave.
$v = \nu \lambda$.

We are given v = 340 m/s and $\nu$ = 256 Hz. Therefore, we can get wavelength as:
$\lambda = \dfrac{v}{\nu}$
$\lambda = \dfrac{340}{256}$
$\lambda = 1.33$ m.

This means that the distance between two successive compressions of the given sound wave is 1.33 m.

So, the correct answer is “Option C”.

Additional Information:
Sound wave is an example of longitudinal wave where the direction of propagation of the wave is the same as the oscillation of a particle in the wave. In a transverse wave, the particles in the wave oscillate perpendicular to the direction of propagation of the wave like in case of vibrating string. Light wave is an example of transverse wave but it does not require any medium for its propagation; it can travel in vacuum too.

Note:
The formula can be derived even with the help of units. The unit of wavelength is meter and that of frequency is Hertz ($s^{-1}$). The unit of velocity is m/s. The obvious relation for these three quantities can directly come from this.