Question

A car moves with a speed of 54 km h−1 towards a cliff. The horn of the car emits sound of frequency 400 Hz at a speed of 335 m s−1. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave? (d) How many beats does he hear in 10 seconds between the sound coming directly from the horn and that coming after the reflection?

Answer 1

Wavelength of sound from horn is 80 cm

Explanation:

• (a) As the car is moving at a speed of 54 kmph =15 $ms^-^1$, the observer will get a slightly decrease in velocity of the sound wave.

$v = v_s_o_u_n_d - v_c_a_r$

$\lambda f = 335 -15 ms^-^1 = 325 ms^-^1$

$\lambda$ = 80 cm

• (b) The frequency near the cliff will be,

f = $\frac {v}{v - v_s}f_0$

f = 418 Hz

$\frac {v}{\lambda}$ = 418

$\lambda = \frac {335}{418}$ = 80 cm

• (c) Frequency of the source will be, $f_0$= 418 Hz

Now,

f = $\frac {v + v_0}{v}f_0$

f = $\frac {335 + 15}{335} \times 418$

f = 437 Hz  

• (d) The frequency difference is

437-400 = 37 beats.

That means it is way higher than 10 beats per second. So, he may not hear anything.