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

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,

⇒  

Where observed frequency, actual frequency, speed of sound, speed of observer, speed of source.

so for first case sonar is source and whale is our observer and we need to put instead of

∴  

Where frequency heard by whale

Hz

For second case whale behave as a source and ship behave as observer and we take

∴  

Where frequency heard by ship

Hz

So difference between these two frequency,

Hz ≅74 Hz

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

double the distance = divide strength by 4