Question

To practice Problem-Solving Strategy 16.2 Doppler effect. 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. mastering physics g

Answer 1

Answer:

147 Hz

Explanation:

First we need to know what frequency will the waves hitting the whale have respect of it.

The change in frequency is calculated with this equation:

$\Delta f = \frac{\Delta v}{c} * f0$

However in this case, the wave is bouncing on the whale and coming back, so there is a double frequency shift (the difference is the same both times because the relative speeds between the two objects is the same both times)

$\Delta f = 2*\frac{\Delta v}{c} * f0$

Then:

$\Delta f = 2*\frac{\4.95 - 0}{1482} * 22000 = 147 Hz$

The frequency shift is positive, it will have increased frequency.