(numbers 18-19) Two fire trucks are at rest and their sirens each emit a single

Question

(numbers 18-19) Two fire trucks are at rest and their sirens each emit a single frequency. You stand at rest in the middle of the trucks and observe a beat frequency of 12.0 Hz. You experimentally determine that running toward truck 1 (away from truck 2) at 8.50 m/s causes the beat frequency to become zero. The speed of sound is 340 m/s 18. What is the frequency emitted by truck 1? a) 117 Hz b) 156 Hz c) 195 Hz d) 234 Hz e) 273 Hz 19. What is the beat frequency if you run toward truck 2 (away from truck 1) at 8.50 m/s? a) 28 b) 24 Hz c) 20 d) 16 Hz e) 12 (numbers 20-21) Two speakers emit the same pure tone (sound of a single frequency) and are in phase. 20. An observer begins at the center point between the speakers and slowly moves toward one of the speakers. The second very quiet spot encountered (completely destrugtive interference) is 2.25 m from the center. What is the wavelength of the sound? a) 1.0 m b) 1.5 m c) 2.0 m 2.5 m e) 3.0 m 21. If the distance between the speakers is 5.5 m, what is the shortest distance from either speaker where a loud spot (completely constructive interference) is found? 0.75 m b) 1.25 m c) 1.75 m d) 2.25 m e) 2.75 m

Explanation / Answer

18. f2 - f1 = 12 Hz ...... (i)

and from Doppler's effect,

f = f0 (v) / (v -+ v_s)  

f2' = f1(340) / (340 + 8.50 )= 340 f1 / 348.5

and f1' = f2(340)/(340-8.50) = 340 f2 / 331.5

f2' = f1'

f2 = 1.05128 f1

putting in (i )

1.05127 f1 - f1 = 12

f1 = 234 Hz .......Ans

19. f2 = 246 Hz

f1' = 234 (340)/(340 + 8.5) = 228.29 Hz

f2' = 246 (340) / (340 - 8.5) = 252.31

beat frequency = f2' - f1' = 24 Hz  

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