Q24 of 29 Page 180

Given that sound travels in air at 340 m/s, find the wavelength of the waves in air produced by a 20kHz sound source. If the same source is put in a water tank, what would be the wavelength of the sound waves in water? Speed of sound in water = 1,480 m/s.

Case 1:

It is given that,


Velocity (v) of sound = 340 m/s.


Wavelength (λ) =?


Frequency (ν) = 20 kHz = 20000 Hz (∵ 1 kHz = 1000 Hz.)


We know that, speed = wavelength × frequency


⇒340 m/s = wavelength × 20000


⇒ Frequency = = 0.017 m.


⇒ Wavelength = 0.017 m.


Case 2:


If the sound source is put in a water tank, the frequency of the waves remains unchanged.


∴ According to the question


Velocity (v) of sound = 1480 m/s.


Wavelength (λ) =?


Frequency (ν) = 20 kHz = 20000 Hz (∵ 1 kHz = 1000 Hz.)


We know that, speed = wavelength × frequency


⇒1480m/s = wavelength × 20000


⇒ Frequency = = 0.074 m.


⇒ Wavelength = 0.074 m.


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