Question

The sound source of a ship’s sonar system operates at a frequency of 22.0 kHz . The speed of sound in water (assumed to be at a uniform 20∘C) is 1482 m/s . What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling straight toward the ship at 4.95 m/s ? Assume that the ship is at rest in the water

Answer 1

Answer:

The difference between the directly radiated waves and waves reflected from a whale is ≅ 74 Hz

Explanation:

Given :

The actual frequency radiated by the ship = 22 kHz = 22000 Hz.

The speed of sound in water = 1482 m/s.

The speed of whale = 4.95 m/s.

According to doppler effect,

⇒  $f = f_{o} (\frac{v-v_{o} }{v-v_{s} } )$

Where $f =$ observed frequency, $f_{o} =$ actual frequency, $v =$ speed of sound, $v_{o} =$ speed of observer, $v_{s} =$ speed of source.

so for first case sonar is source and whale is our observer and we need to put $-v_{o}$ instead of $+v_{o}$

∴  $f_{w } = 22000 (\frac{1482+4.95}{1482} )$

Where $f_{w} =$ frequency heard by whale

$f_{w} = 22073$ Hz

For second case whale behave as a source and ship behave as observer and we take $+v_{s}$

∴   $f_{s} = 22073(\frac{1482}{1482-4.95} )$

Where $f_{s} =$ frequency heard by ship

$f_{s} = 22146.9$ Hz

So difference between these two frequency,

$f_{s} - f_{w} = 73.9$ Hz ≅74 Hz

Thus, the difference between the directly radiated waves and waves reflected from a whale is ≅ 74 Hz.