Peoples Physics Concepts

http://www.ck12.org Chapter 11. Wave Motion and Sound

11.4 Doppler Effect

• Describe the Doppler effect and use the Doppler shift equations to determine frequencies and speeds.

Students will learn what the Doppler effect is and how to determine frequencies and speeds using the Doppler shift

equations.

Key Equations

Doppler Shifts:

fo=f

v+vo

v−vs

fo(observed frequency)is shifted up when source and observer moving closer

fo=f

v−vo

v+vs

fo(observed frequency)is shifted down when source and observer moving apart,where

vis the speed of sound,vsis the speed of the source, andvois the speed of the observer

Guidance

TheDoppler Effectoccurs when either the source of a wave or the observer of a wave (or both) are moving. When a

source of a wave is moving towards you, the apparent frequency of the wave you detect is higher than that emitted.

For instance, if a car approaches you while playing a note at 500 Hz, the sound you hear will be slightly higher

frequency. The opposite occurs (the frequency observed is lower than emitted) for a receding wave or if the observer

moves away from the source. It’s important to note that the speed of the wave does not change –it’s traveling through

the same medium so the speed is the same. Due to the relative motion between the source and the observer the

frequency changes, but not the speed of the wave. Note that while the effect is similar for light and electromagnetic

waves the formulas are not exactly the same as for sound.

Example 1

Question: How fast would a student playing an A note (440Hz) have to move towards you in order for you to hear

a G note (784Hz)?

Answer: We will use the Doppler shift equation for when the objects are getting closer together and solve for the

speed of the student (the source).

fo=f(

v+vo

v−vs

)⇒fo×(v−vs) =f×(v+vo)⇒v fo−vsfo=f×(v+vo)⇒vs=−(

f×(v+vo)−v fo

fo

)

Now we plug in the known values to solve for the velocity of the student.

vs=−(

f×(v+vo)−v fo

fo

) =−(

440Hz×(343m/s+0m/s)−343m/s×784Hz

784Hz

) =151m/s