A sound wave has a frequency of 1 kHz and wavelength 50 cm. How long will it take to travel 1 km?

CONCEPT:

• The sound waves propagate through the air in different frequencies, among this human ears can only sense the sound of bandwidth 20 Hz-20 kHz.
• Sound waves with a frequency greater than audible waves are known as Ultrasonic waves.
• The wavelength of this wave can be defined as displacement made when a wave completes its one oscillation
• And the relation between wavelength (λ), frequency (n), and velocity (v) can be given as

v = n × λ      ,,,,(1)

• Since the frequency (n) of the sound wave will be inverse of the time period (T) so the above equation will become,

\(⇒ T=\frac{d}{v}\;\;\;\;\; \ldots \left( 2 \right)\)

Where, n = Frequency of the sound wave, λ = Wavelength of the sound wave, d = Distance traveled by the sound wave in T time moving with velocity v

CALCULATION:

Given: n =1 kHz, λ = 50 cm = 0.5 m, d = 1 km = 1000 m

• Using equation 1, the velocity of sound in air,

⇒ v = n × λ = 1000 × 0.5 = 500 m/s

• Using equation 2,

\(⇒ T=\frac{1000}{500}=2 \ sec\)

⇒ T = 2 sec

So, the correct answer will be option 4.