Question

If you move at 18 m/s towards a 2300 -Hz source that is moving towards you with a ground speed of 30 m/s, what frequency do you hear?

Answer 1

The frequency you will hear is 2,639.7 Hz

Step-by-step explanation:

Given;

source frequency, Fs = 2300 Hz

velocity of the source, Vs = 30 m/s

observed velocity, Vo = 18 m/s

speed of sound in air, V = 343 m/s

Apply Doppler effect, the frequency you will hear is known as observed frequency;

The observed frequency will be greater than the source frequency, since the distance between the source and the observer decreases.

`F_s = F_0((V- V_0)/(V + V_s) )\\\\2300 = F_0 ((343 - 18)/(343 + 30) )\\\\2300 = F_0((325)/(373) )\\\\F_0= 2300((373)/(325)) \\\\F_0 = 2,639.7 \ Hz`

Note: the aim is to increase the observed frequency.

Subtracting the observed speed from the speed of sound for the numerator will ensure an increase in the observed frequency, also adding the source speed to the speed of sound for the denominator will equally ensure an increase in the observed frequency.