Question

Question: A particular vehicle produces sound by setting up the fundamental standing wave in an air column 7.10 cm long. The tube is closed at one end. The whistle blower is riding in a car moving away from you at 25 m/s. What frequency do you hear?

Short answer

The frequency of hearing is \(1130\;{\rm{Hz}}\).

Step-by-step solution

Determination of frequency of sound

For a moving object, the hearing frequency depends upon the velocities of the object and the velocity of sound. This effect is known as Doppler’s shift.

Given Information

Given data:

The length of air column is \(l = 7.10\;cm\).

The speed of the car is \({v_{{\rm{source}}}} = 25\;{{\rm{m}}}\)/s.

The velocity of sound is v_snd = 343 m/s.

Find the frequency of the sound wave using Doppler’s effect

The expression for the fundamental frequency is given as:

\({f_1} = \frac{{{v_{{\rm{snd}}}}}}{{4l}}\)

The frequency in a closed tube with the Doppler’s shift for a source moving away from the stationary observer is given as:

Thus, the frequency of hearing is \(1130\;{\rm{Hz}}\).