Q48P - University Physics with Modern Physics

Question

A loudspeaker with a diaphragm that vibrates at 960 Hz is traveling at 80.0 m/s directly toward a pair of holes in a very large wall. The speed of sound in the region is 344 m/s. Far from the wall, you observe that the sound coming through the openings first cancels at ±11.4° with respect to the direction in which the speaker is moving. (a) How far apart are the two openings? (b) At what angles would the sound first cancel if the source stopped moving?

Step-by-Step Solution

Answer

1. The two openings are 71cm
2. The angle of the sound first cancels if the source stopped moving is $14.9°$

Step 1: Diffraction by a single slit

Diffraction by a single slit is given by;

Step 2: Doppler effect

As the source and observer move towards (or away from) each other, the frequency of sound, light, or other waves increases (or decreases);

Here, f is the frequency of the sound that approaches the wall and passes through holes.

Step 3: Distance between the two openings

    1. Given;

     

         Distance is

       

    Hence, the two openings are 71cm.

Step 4: Angles the sound first cancel if the source stopped moving

(b) If the singer were to stop, the frequency of sound approaching the wall would be $f_0$, and the angle $\theta$ at which the first destructive interference.

             

     On substituting;

Putting the values;

Hence, the angle of the sound first cancels if the source stopped moving is $14.9°$