Question

A car traveling 37.0 m/s overtakes another car going only 21.0 m/s. When the faster car is still behind the slower one, it sounds a horn of frequency 1400.0Hz. What is the frequency heard by the driver of the slower car?

Answer 1

Sound propagates at a speed of about 1,100 feet per second in air at sea level and the sound is in the form of sinusoidal waves at a frequency depending upon the source (horn). In a way, sound spreads like the ripples on a still mill pond when you throw in a stone. If a swimmer swims toward the stone, he/she will encounter more ripples per second than if standing still and less ripples per second if swimming away from the stone. The pitch of the "sound" depends on the ripples per second encountered.

In your example, the driver is moving much slower than the sound waves (which are traveling at Mach one, like a jet plane!). If the car was still the pitch of the horn would be F1 (frequency 1). If the car approaches the listner the pitch increases to F2 because each new wave originates closer and closer to the listener and has less far to travel. If the driver and listener are traveling in the same direction at the same speed, the drivers pitch increases from F1 to F2 but the listener's motion shifts the pitch back from F2 to F1 because the time it takes each wave to travel to the listener is the same as if both were at rest. The distance between them is constant if they are at rest or traveling at the same speed in the same direction. Of course if both the driver and the listener are traveling at the speed of sound in the same direction, the sound would never reach the listener.

Doppler effect

No

The formula goes something like this

Fo= intial frequency
F=Heard frequency
V=speed of sound
Vs=speed of source
Vo=speed of observer

F=Fo*(V-Vs)/(V-Vo)

so lets plug in some make believe numbers.

Fo=10...... V=100.......Vs=30...... Vo=30

F=10*(100-30)/(100-30)=10