THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 8:
 
WAVES I
 
Wed. 8 Nov. 2000 - finish by Wed. 15 Nov.

1.

Travelling Wave in a String: We are observing a string whose transverse displacement  y  is given [in ${\cal SI}$ units] as a function of time  t  and position  z  (down the length of the string) by

$$y(z,t) \; = \; 4.73 \sin(7z - 5t) \; + \; 7.22 \cos(7z - 5t)$$

(a)

In what direction is the wave traveling?

(b)

What is the amplitude of the traveling wave?

(c)

What is the frequency of ${\cal SHM}$ at any point on the string?

(d)

What is the wave propagation velocity on the string?

2.

Power in a Wavy String: If a continuous transverse sinusoidal wave of amplitude A is propagating down a taut string of linear mass density $\mu$ at velocity v with frequency $\omega$, show that the power transmitted in the wave is   $P = {1\over2} \mu \, \omega^2 A^2 \, v$.

3.

Double Doppler Effect: Sound waves are emitted by a source moving at v_s directly toward a detector which in turn is moving directly toward the source at a speed v_d. Both v_s and v_d are less than the speed of sound c. If $f_\circ$ is the frequency at which the sound is emitted in the rest frame of the source, show that the frequency f which is detected by the moving detector is given by ${\displaystyle f = f_\circ \left( c + v_d \over c - v_s \right) }$ .

. . . and Tipler (4$^{\rm th}$ Edition)

Ch. 15: problems 22, 32, 98, 101, 118 and 121

Ch. 16: problems 11, 65 and 75