THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 2:
 
WAVES II

12 Jan. 2000 - finish by 17 Jan. 2000

Tipler Ch. 13, problems 25, 51, 57 & 67;

1.

Generalization of Doppler Effect: A sound emitter (``source'') moves directly toward an observer at velocity v<c (where c is the speed of sound); at the same time, the observer moves directly toward the emitter at velocity u<c. Show that the frequency f' of the sound heard by the observer is given by ${\displaystyle f' = f \left[ c + u \over c - v \right] }$, where f is the frequency heard by the emitter, and that this formula is also correct for negative v (emitter receding from receiver) and/or negative u (receiver receding from emitter) as long as |v|<c and |u|<c. [The textbook states this fact; you prove it is valid.]

Hint: Think in terms of wave crests, as illustrated in the sketch above.
How much does the source ``catch up'' with one wave crest before it emits the next one?
How fast do the waves seem to be moving relative to the moving observer?

For the Brave: Try doing the derivation for arbitrary vector velocities $\vec{v}$ and $\vec{u}$ and for arbitrary positions $\vec{r}_s$ and $\vec{r}_o$ of the source and observer. If you can do this, you can get a job designing radar guidance systems . . . .

. . . and Tipler Ch. 14, problems 21, 33 & 35.