Question

(1) (A)You approach a stationary sound source with a speed such that the frequency of sound you hear is 17% greater than the actual frequency. With what speed are you approaching the sound source? Use the speed of sound in air as 343 m/s.

(B)Two trains approach each other on separate but adjacent tracks. Train 1 is traveling at a speed of 31.9 m/s and train 2 at a speed of 27.6 m/s. If the engineer of train 1 sounds his horn which has a frequency of 520 Hz, determine the frequency of the sound heard by the engineer of train 2. (Use 343 m/s as the speed of sound. Enter your answer to the nearest Hz.)

(C)Alice holds a small battery operated device used for tuning instruments that emits the frequency of middle C (262 Hz) while walking with a constant speed of 3.38 m/s toward a building which presents a hard smooth surface and hence reflects sound well. (Use 343 m/s as the speed of sound in air.) (A) Determine the beat frequency Alice observes between the device and its echo. (Enter your answer to at least 1 decimal place.) (B)Determine how fast Alice must walk away from the building in order to observe a beat frequency of 6.59 Hz.
m/s

Answer 1

1)

Using doppler's effect of sound

F_observed = F_emitted {V+V_o}/{V-V_s}

where V is the speed of sound ,

V_o is the speed of the observer

V_s is the speed of the source

substitute the given values in above formula, we get

1.17 F = F (343+V_o)/(343+0)

1.17 = (343 +V_o )/343

therefore , V_o = 58.31 m/s (your speed towards the stationary source)

2) Again substitute the given values in the above stated formula for the doppler's effect for sound :

F = 520 (343+27.6)/(343-31.9)

F = 520* 1.19125

F = 619.45 Hz

Therefore , the frequency heard by the engineer of train 2 = 619 Hz.

3) using the doppler's effect of sound for reflected sound as :

F_observed = F_emitted (V+V_0)(V+V_s)/[(V-V_s)(V-V_o)]

F_observed = 262*(343+0)(343+3.38)/(343-3.38)(343+0)

F_observed = 267.215 Hz

Therefore, Beat frequency = 267.215 - 262 = 5.2 Hz

case B ) beat frequency 6.59 Hz

therefore the observed frequency = 262 - 6.59 = 255.41

substituting these values in the above formula

255.41= 262*(343+0)(343-v)/(343+v)(343+0)

255.41 = 262 {[343-v]/[343+v]}

0.974847 v + 334.3726 = 343 - v

v = 4.368 m/s

v = 4.4 m/s

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