   Chapter 14, Problem 65P

Chapter
Section
Textbook Problem

Two train whistles have identical frequencies of 1.80 × 102 Hz. When one train is at rest the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 2.00 beats/s when the whistles operate together. What are the two possible speeds and directions that the moving train can have?

To determine
The two possible speeds and directions that the moving train can have.

Explanation

Given Info: Trains whistle at frequency 1.80×102Hz , frequency of the beat heard is

2.00beats/s .

Formula to calculate the beat frequency is,

fB=|f1f2|

• fB is the beat frequency.
• f1 is the frequency of the whistle from first train as heard by the commuter (stationary).
• f2 is the frequency of the whistle from second train as heard by the commuter (stationary).

Formula to calculate the frequency of the whistle from second train f2 as heard by the commuter is,

f2=f1±fB

Substitute 1.80×102Hz for f1 and 2.00Hz for fB to find f2 .

f2=1.80×102Hz±2.00Hz=180Hz±2.00Hz=178Hzor182Hz

The lower frequency is heard when the second train moves away from the station and higher frequency is heard when the second train moves towards the station.

Formula to calculate the speed of the second train moving away from the station is,

v2=vsound[f1f21]

• vsound is the velocity of sound in air.

Substitute 343m/s for vsound , 180 Hz for f1 , and 178 Hz for f2 to find v2

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