MORE  WAVES

1.

Each of two adjacent loudspeakers produces a pure note (a single frequency sound wave). A microphone in the same room detects the sound intensity as a function of time and the result is plotted on an oscilloscope as a function of time, as pictured in the graph below. [Note: ms = milliseconds.]

From the graph, estimate the frequency of each of the two transmitters. Express your answer in kHz [kilohertz].

2.

Two piano strings of equal length have fundamental frequencies (for transverse vibrations) of 440 Hz. If the tension in the first string drops by 1 %, what beat frequency will the listener hear when both strings are struck simultaneously?

3.

A string has a length of 80 cm and a mass of 4 g. It is fixed at both ends. What must its tension be in order for its next-to-lowest transverse vibration frequency to be 440 Hz?

4.

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

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

(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?

5.

A speedboat moving as shown at 80 km/h emits a 220 Hz sound. What frequency is detected by the stationary microphone at point A?