Question

A bat flies at a steady rate of 4 m/s emitting 90 kHz sound wave and is flying towards a wall.It detects a reflected signal at s frequency………….kHz.Given speed of sound=340m/s.
a)90.1 b)92.1 c)91.1 d)93.1

Answer 1

Answer on Question#38156 – Physics – Other

A bat flies at a steady rate of $4\,\mathrm{m/s}$ emitting $90\,\mathrm{kHz}$ sound wave and is flying towards a wall. It detects a reflected signal at a frequency...kHz. Given speed of sound=340m/s.

a)90.1 b)92.1 c)91.1 d)93.1

Solution:

The bat hears $f_w$ coming from the wall. If $v = 4\,\frac{\mathrm{m}}{\mathrm{s}}$ is the magnitude of bat speed, $V = 340\,\frac{\mathrm{m}}{\mathrm{s}}$ is a speed of sound and $f_w$ the frequency the wall receives (and reflects). Bat is moving source and wall is stationary observer.

$$\frac{V}{f_w} = \frac{V - v}{90\,\mathrm{kHz}}$$

Solve equation relative to $f_w$:

$$f_w = \frac{90\,\mathrm{kHz} \cdot V}{V - v} = \frac{90\,\mathrm{kHz} \cdot 340\,\frac{\mathrm{m}}{\mathrm{s}}}{340\,\frac{\mathrm{m}}{\mathrm{s}} - 4\,\frac{\mathrm{m}}{\mathrm{s}}} = 91.1\,\mathrm{kHz}$$

Answer: c) $91.1\,\mathrm{kHz}$