(a) What frequency is received by a person watching an oncoming ambulance moving at 105 km/h and emitting a steady 853 Hz sound from its siren?
(a) f' = 878 Hz
When an ambulance is moving towards a person, the sound waves emitted from its siren will be compressed due to the motion of the ambulance. This compression of sound waves leads to an increase in frequency, which is known as the Doppler Effect.
Explanation:
The Doppler Effect: The Doppler Effect is a phenomenon where the frequency of a wave appears to change when there is relative motion between the source of the wave and the observer. In this case, as the ambulance is moving towards the person, the sound waves are compressed, leading to a higher perceived frequency.
Calculation: The formula to calculate the new frequency (f') when there is relative motion is given by:
f' = f * (v + v_o) / (v - v_s)
where:
f = frequency of the source (853 Hz)
v = speed of sound in air (343 m/s)
v_o = speed of the observer (0 m/s, since the person is stationary)
v_s = speed of the source (105 km/h = 29.17 m/s)
Plugging in the values, we get:
f' = 853 * (343 + 0) / (343 - 29.17) = 878 Hz
Therefore, the frequency received by a person watching an oncoming ambulance moving at 105 km/h and emitting a steady 853 Hz sound from its siren is 878 Hz.