Chapter 16: Q.42 (page 452)

An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 90 km/h. What is the frequency heard by a. A person standing beside the road in front of the car? b. A person on the ground behind the car?

Expert verified

Part a

Frequency of sound as her convertible approaches the stationary observer is $650 H z$ .

Part b

Frequency of sound as her convertible recedes the stationary observer is $560 H z$ .

Step by step solution

The opera singer sings a note at $f_{0} = 600 H z$ .

The speed of an opera singer $v_{s} = 90 k m / h r = 25 m / s$ .

Speed of sound is $v = 343 m / s$

Doppler effect for an approaching source is given by $f_{+} = \frac{f_{0}}{1 - \frac{v_{s}}{v}}$ .

The frequency as her convertible approaches the stationary observer is

$f_{+} = \frac{600}{1 - \frac{25}{343}} \approx 650 H z$

Therefore, the frequency of sound as her convertible approaches the stationary observer is $650 H z$ .

Doppler effect for a receding source is given by $f_{-} = \frac{f_{0}}{1 + \frac{v_{s}}{v}}$ .

The frequency as her convertible recedes the stationary observer is

$f_{-} = \frac{600}{1 + \frac{25}{343}} \approx 560 H z$

Therefore, the frequency of sound as her convertible recedes to the stationary observer is $560 H z$ .

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