1 ) At a factory, a noon whistle is sounding with a frequency of 451 Hz. As a ca

Question

1 ) At a factory, a noon whistle is sounding with a frequency of 451 Hz. As a car traveling at 84 km/h approaches the factory, the driver hears the whistle at frequency fi. After driving past the factory, the driver hears frequency ff. What is the change in frequency ff - fi heard by the driver? (Assume a temperature of 20° C.) unit in HZ

2 ) A source of sound waves of frequency 0.9 kHz is traveling through the air at 0.75 times the speed of sound.

(a) What is the frequency of the sound received by a stationary observer if the source moves toward her? unit in khz

(b) Now, the source moves away from the stationary observer. What is the frequency of the sound received in this case? unit in KHZ

Explanation / Answer

(1) Data: Frequency, f = 451 Hz Speed of the car, vo = 84 km/h                                 = 84 * (5/18) m/s                                 = 23.33 m/s Speed of the sound, v = 343 m/s Solution: Approaching the factory: Observed frequency, fi = [ ( v + vo ) / v ] * f                                     = [ ( 343 + 23.33) / 343 ] * 451                                     = 481.7 Hz Receding the factory: Observed frequency, ff = [ ( v - vo ) / v ] * f                                     = [ ( 343 - 23.33) / 343 ] * 451                                     = 420.3 Hz Change in frequency = ff - fi                                 = 481.7 Hz - 420.3 Hz                                 = 61.4 Hz Ans: Change in frequency = 61.4 Hz (2) Data: Frequency, f = 0.9 kHz                     = 900 Hz Speed of sound = v Speed of the source, vs = 0.75 v Solution: (a) Observed frequency, fo = [ v / ( v - vs ) ] * f                                      = [ v / ( v - 0.75 v ) ] * 900                                      = 3600 Hz Ans: Observed frequency, fo = 3600 Hz (or) 3.6 kHz (b) Observed frequency, fo = [ v / ( v + vs ) ] * f                                      = [ v / ( v + 0.75 v ) ] * 900                                      = 514.3 Hz Ans: Observed frequency, fo = 514.3 Hz (or) 0.514 kHz Approaching the factory: Observed frequency, fi = [ ( v + vo ) / v ] * f                                     = [ ( 343 + 23.33) / 343 ] * 451                                     = 481.7 Hz Receding the factory: Observed frequency, ff = [ ( v - vo ) / v ] * f                                     = [ ( 343 - 23.33) / 343 ] * 451                                     = 420.3 Hz Receding the factory: Observed frequency, ff = [ ( v - vo ) / v ] * f                                     = [ ( 343 - 23.33) / 343 ] * 451                                     = 420.3 Hz Change in frequency = ff - fi                                 = 481.7 Hz - 420.3 Hz                                 = 61.4 Hz Ans: Change in frequency = 61.4 Hz (2) Data: Frequency, f = 0.9 kHz                     = 900 Hz Speed of sound = v Speed of the source, vs = 0.75 v Solution: (a) Observed frequency, fo = [ v / ( v - vs ) ] * f                                      = [ v / ( v - 0.75 v ) ] * 900                                      = 3600 Hz Ans: Observed frequency, fo = 3600 Hz (or) 3.6 kHz (b) Observed frequency, fo = [ v / ( v + vs ) ] * f                                      = [ v / ( v + 0.75 v ) ] * 900                                      = 514.3 Hz Ans: Observed frequency, fo = 514.3 Hz (or) 0.514 kHz Observed frequency, fo = [ v / ( v + vs ) ] * f                                      = [ v / ( v + 0.75 v ) ] * 900                                      = 514.3 Hz Ans: Observed frequency, fo = 514.3 Hz (or) 0.514 kHz

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