Question

A sound source producing 1.00 kHz waves moves toward a stationary listener at one-half the speed of sound.
a) What frequency will the listener hear?
(b) Suppose instead that the source is stationary and the listener moves toward the source at one half the speed of sound. What frequency does the listener hear? How does your answer compare with that in par a? Did you expect to get the same answer in both cases? Explain on physical grounds why the two answers differ

Answer 1

Answer:

2000Hz and 1500Hz

Explanation:

Using

a) f = f0((c+vr)/(c+vs))

=>>> f0((c)/(c-0.5c))

=>>>1000/0.5 = 2000Hz

b) f = f0((c+vr)/(c+vs))

=>>>f0((c+0.5c)/(c))

=>>>>1000 x 1.5 = 1500Hz

Answer 2

Here we have a problem referring to the Doppler effect, the solutions are:

• a) f = 2.0 kHz
• b) f = 1.5 kHz

The Doppler effect:

The Doppler effect is an effect that explains how the perception of waves changes as the source moves or as the listener moves.

The formula, for sound, is:

$f = \frac{v + v_0}{v - v_1}*f_0$

where:

• v = velocity of the wave = 340 m
• f = perceived frequency
• f₀ = actual frequency = 1.00kHz
• v₀ = velocity of the observer
• v₁ = velocity of the source.

a) First we have that the source moves towards a stationary listener, then we have:

$f = \frac{v }{v - v/2}*1.0 kHz\\\\f = \frac{v }{v/2}*1.0 kHz = 2.0 kHz$

b) in this case, the listener moves towards the source, so we have:

$f = \frac{v + v/2 }{v }*1.0 kHz\\\\f = \frac{ (3/2)*v }{v}*1.0 kHz = 1.5 kHz$

So in this case the perceived frequency is smaller than in the point a.

This is because the waves will move at a fixed rate in air, in one case, the successive waves are emitted from different points in space (each time closer to the listener) while in the other case the waves are emitted from a fixed point, and the listener moves towards them, thus feels that the waves move faster.

If you want to learn more about the Doppler effect, you can read:

https://brainly.com/question/3826119