You are driving down the road heading north at 15 m/s. An ambulance is driving in the opposite direction (south) towards you at 25 m/s. If the ambulance's siren emits sound at a frequency of 2 kHz, what frequency do you hear? Assume that the speed of sound is 340 m/s.
To calculate the frequency of the sound you hear, we can use the formula for the Doppler effect:
f' = f * (v + vo) / (v + vs)
where:
f' = frequency heard by the observer
f = frequency emitted by the source
v = speed of sound
vo = speed of the observer
vs = speed of the source
Plugging in the values we know:
f = 2 kHz = 2000 Hz
v = 340 m/s
vo = 15 m/s (you)
vs = 25 m/s (ambulance)
f' = 2000 * (340 + 15) / (340 - 25)
f' = 2000 * 355 / 315
f' = 2000 * 1.1269
f' = 2253.8 Hz
Therefore, you will hear a frequency of 2253.8 Hz.