Concept #1: The Doppler Effect

Practice: A police siren emits a sound somewhere around 700 Hz. If you are waiting at a red light, and a police car approaches you from behind and passes you, moving at a constant 30 m/s, what is the frequency you hear from the siren as it approaches you from behind? What about once it’s passed you? Assume the air temperature to be 20°C.

Example #1: Two Submarines Approaching One Another

An object emitting a sound at a constant frequency is thrown into the air. As the source travels up and back down again, the frequency you hear is going to change via the Doppler effect. Assuming the source is always above your ear, which of the following statements if true:
(a) The frequency heard will start at a maximum and decrease through the entire trip
(b) The frequency heard will start at some value, decrease to a minimum value as it rises, and then increase back to its starting value as it falls
(c) The frequency heard will start at some value, increase to some maximum value as it rises, and then decrease back to its starting value as it falls
(d) The frequency heard will start at a minimum and increase through the entire trip

Two speakers, A and B, are moving towards each other with a closing speed of 30 m/s, meaning the distance separating the two speakers is decreasing by 30 m every second. At rest, speaker A emits a frequency of 150 Hz and speaker B emits a frequency of 200 Hz. For all questions, assume the speed of sound is 340 m/s.
(a) From speaker A's perspective, what is the frequency of speaker B?
(b) From speaker B's perspective, what is the frequency of speaker A?
(c) If an observer were standing in between the two speakers, and speaker A were moving towards him with a speed of 10 m/s, what beat frequency would the observer hear?

A police car is traveling at a speed vc to the right and a truck is traveling at a speed vt to the right. The frequency of the siren on the police car is fc.
What is the frequency ft heard by an observer in the moving truck? Let vt be the speed of the observer in the truck, and vc be the speed of the source, the police car. The speed of sound in air is va.

An ambulance is traveling North at 54.3 m/s, approaching a car that is also traveling North at 33.6 m/s. The ambulance driver hears his siren at a frequency of 678 cycles/s. The velocity of sound is 343 m/s. At what frequency does the driver of the car hear the ambulance's siren?