Speakers A and B emit a pure sinusoidal tone of frequency 11

Speakers A and B emit a pure sinusoidal tone of frequency 110 Hz and are in phase. The speed of sound is 330 m/s. The speakers are 4 m apart. What is the closest position to speaker A along a line connecting speakers A and B where an observer will find completely destructive interference from the two sources? 1.25 m 1.5 m 1.75 m 2.0 m 2.5 m Two fire trucks each emit a sound of 1000 Hz. One moves away from you at 20 m/s and the other moves toward you at 20 m/s. The speed of sound is 340 m/s. You are stationary. What beat frequency do you observe when hearing the sirens simultaneously? 38 Hz 58 Hz 78 Hz 98 Hz 118 Hz

Solution

31) Let x be the distance from speaker A.

The distance from speaker B is 4-x.

Path difference is 4-x-x=4-2x.

For destructive interference, this should be equal to half of the wavelength.

4-2x=.5*(330/110)=1.5

So, 2x=2.5.Therefore ,x =1.25

32) The frequencies are: (340/(340+20))*1000 = 944.44Hz

and ((340)/(340-20))*1000 = 1062.5Hz

Beat frequency is 1062.5-944.4 = 118HHz approx