Question

At what speed a car is approaching a stationary observer. if he hears the sound of a car siren with the frequency of 10% higher than the actual frequency. The speed of sound is 340 m/S.

Answer 1

Answer:

V = speed of sound = 340

v = speed of car

f = actual frequency        f' = observed frequency

y = actual wavelength     y' = observed wavelength

y - y' = v T    wavelength minus distance car travels in 1 period (T)

f' / f = 1.1     so T / T' = 1.1    

y - y' = v T          and     y = V / f = V T

V T - V T' = v T

v = V (T - T') / T = 340 * (1 - 1 / 1.1) = 30.9 m/s

Or you can use the Doppler formula for a moving source

f' = f V / (V - v)

Checking the value found then

f' / f = 1.1 = 340 / (340 - 30.9)     which agrees