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

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

Step-by-step 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) ((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 ((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((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.