Question

A car honks its horn as it approaches you. The car is traveling at 16. m/s and the horn has a frequency of 900. Hz. What frequency do you hear?

A) 860 Hz
B) 900 Hz
C) 944 Hz
D) 990 Hz

Answer 1

Answer on Question #47927 – Physics – Mechanics | Kinematics | Dynamics

A car honks its horn as it approaches you. The car is traveling at 16 m/s and the horn has a frequency of 900 Hz. What frequency do you hear?

A) 860 Hz

B) 900 Hz

C) 944 Hz

D) 990 Hz

**Solution:**

$v_{s} = 16\frac{m}{s}$ – velocity of the source (velocity of the car);

$v_{d} = 0$ – velocity of the receiver (your velocity);

$v = 343\frac{m}{s}$ – speed of sound;

$f_{0} = 900\, \text{Hz}$ – frequency of the horn;

$f$ – frequency that you hear;

This is Doppler effect problem.

As the car approaches, the sound waves will have shorter wavelengths and higher frequencies, and as it goes by, the sound waves will have longer wavelengths and lower frequencies.

In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency $f$ and emitted frequency $f_0$ is given by

$$f = \left(\frac{v - v_d}{v - v_s}\right) f_0 = 900\, \text{Hz} \left(\frac{343\frac{m}{s} - 0}{343\frac{m}{s} - 16\frac{m}{s}}\right) = 944\, \text{Hz}$$

Answer: C) 944 Hz

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