Question

What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?

a) (a) (850 Hz); (b) (750 Hz)
b) (a) (900 Hz); (b) (700 Hz)
c) (a) (950 Hz); (b) (650 Hz)
d) (a) (1000 Hz); (b) (600 Hz)

Answer 1

The observed frequency of an approaching ambulance siren using the Doppler Effect is approximately 895 Hz. After it passes and is moving away, the observed frequency is approximately 758 Hz. Hence, the closest answer is (a) (900 Hz); (b) (700 Hz).

Step-by-step explanation:

The frequency received by a person watching an oncoming ambulance can be calculated using the Doppler Effect formula for a source moving toward an observer:

f' = f(v + vo) / (v)

Where:

• f' is the observed frequency.
• f is the source frequency (800 Hz).
• v is the speed of sound (345 m/s).
• vo is the speed of the observer relative to the medium, which is 0 since the observer is stationary.
• vs is the speed of the source (ambulance), which is 110 km/h or 30.56 m/s when converted.

Plugging the values into the formula:

f' = 800 Hz (345 m/s + 0) / (345 m/s - 30.56 m/s)

f' ≈ 895 Hz

For part (b), when the ambulance is moving away, the formula is:

f' = f(v - vo) / (v + vs)

Plugging in the values:

f' = 800 Hz (345 m/s - 0) / (345 m/s + 30.56 m/s)

f' ≈ 758 Hz

Therefore, the correct answer is closest to option (b), which is (a) (900 Hz); (b) (700 Hz).