Question

A car moving at 108 km h−1 finds another car in front it going in the same direction at 72 km h−1. The first car sounds a horn that has a dominant frequency of 800 Hz. What will be the apparent frequency heard by the driver in the front car? Speed of sound in air = 330 m s−1.

Answer 1

Apparent Frequency is 827 Hz

Explanation:

Given,  

• Horn Sounding Velocity, $v_s = 108\ kmhr^-^1$

= $108 \times \frac {5}{18}\ ms^-^1 = 30 ms^-^1$

• Frontal car Velocity, $v_0 = 72\ kmhr^-^1$

= $72 \times \frac {5}{18}\ ms^-^1 = 20 ms^-^1$

Frequency, $f_0 = 810\ Hz$

Air Velocity, v = $330\ ms^-^1$

• In front car the driver hears the sound with apparent frequency,  

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

Subtituting the values in above equation-

f = $\frac {330 - 20}{330 - 30} \times 800$

= 826.67 or 827 Hz