|You hear the effect of a Doppler
shift in frequency every time a car goes by. But what happens to produce a sonic
boom when a fast jet goes by? This short exercise below will shed some light on the idea
(yes! Doppler works for light too!).
The animation below shows the sound wavefronts
eminating from a moving source. Begin this exercise by slowing down the source, when about
mid stream, until it is stationary . (The value next to the slider shows the speed of the
source relative to the speed of the waves.)
- Use your watch to help calculate the frequency of the waves
(cycles/sec). Also work out the speed of the waves (cm/sec)
by measuring a distance on the screen using a ruler.
- Slowly increase the speed of the source to about 0.5. Does the speed
of the wavefronts change? Explain this.
- At a speed of 0.5, use your watch to help you calculate the frequency of the wave
observed by a stationary observer just in front of the
source, and another one just behind the source. What
pitch would these people hear compared with when the source was not moving at all?
- Compare these two frequencies with those you get using the Doppler expression in Section
12.8 of the text by Giancoli.
- Increase the speed until the waves in front of the source don't quite manage to get away
from the moving source. What is the speed of the source compared to that of the waves now?
- Finally, increase the speed of the source until it is about 1.5 times that of the waves.
Observe the shock wave that is produced (this is also
referred to as the sonic boom). Stop the motion at a
convenient point and sketch this effect.
(Design of exercise: Jon M Pearce;
Creation of applet: Wolfgang Christian)