PRACTICE IT Use the worked example above to help you solve this problem. A train at a speed of 36.4 m/s sounds it whistle, which has a frequency of 5.06 x 10² Hz. Determine the frequency heard by a stationary observer as the train approaches the observer. The ambient temperature is 21.7°C. Hz EXERCISE HINTS: GETTING STARTED I'M STUCK! Determine the frequency heard by the stationary observer as the train recedes from the observer. frequency = Hz

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EXAMPLE 14.4
GOAL Solve a Doppler shift problem when only the source is moving.
Listen, but Don't Stand on the Track
PROBLEM A train moving at a speed of 40.0 m/s sounds its whistle, which has a frequency of
5.00 x 10² Hz. Determine the frequency heard by a stationary observer as the train approaches the
observer. The ambient temperature is 24.0°C.
STRATEGY Get the speed of sound at the ambient temperature using the relevant equation, then
substitute values into the Doppler shift equation. Because the train approaches the observer, the observed
frequency will be larger. Choose the sign of vs to reflect this fact.
SOLUTION
Calculate the speed of sound in air at T
= 24.0°C.
The observer is stationary, so vo = 0.
The train is moving toward the
observer, so vs = 40.0 m/s (positive).
Substitute these values and the speed
of sound into the Doppler shift
equation.
V = (331 m/s) √T/ 273 K
= (331 m/s) √(273 + 24.0) K/ 273 K =
$ (v + √² ) =
fo=fs (
= 566 Hz
= (5.00 x 10² Hz)
345 m/s
345 m/s
345 m/s - 40.0 m/s
Transcribed Image Text:EXAMPLE 14.4 GOAL Solve a Doppler shift problem when only the source is moving. Listen, but Don't Stand on the Track PROBLEM A train moving at a speed of 40.0 m/s sounds its whistle, which has a frequency of 5.00 x 10² Hz. Determine the frequency heard by a stationary observer as the train approaches the observer. The ambient temperature is 24.0°C. STRATEGY Get the speed of sound at the ambient temperature using the relevant equation, then substitute values into the Doppler shift equation. Because the train approaches the observer, the observed frequency will be larger. Choose the sign of vs to reflect this fact. SOLUTION Calculate the speed of sound in air at T = 24.0°C. The observer is stationary, so vo = 0. The train is moving toward the observer, so vs = 40.0 m/s (positive). Substitute these values and the speed of sound into the Doppler shift equation. V = (331 m/s) √T/ 273 K = (331 m/s) √(273 + 24.0) K/ 273 K = $ (v + √² ) = fo=fs ( = 566 Hz = (5.00 x 10² Hz) 345 m/s 345 m/s 345 m/s - 40.0 m/s
PRACTICE IT
Use the worked example above to help you solve this problem. A train at a speed of 36.4 m/s sounds it
whistle, which has a frequency of 5.06 x 10² Hz. Determine the frequency heard by a stationary observer
as the train approaches the observer. The ambient temperature is 21.7°C.
Hz
EXERCISE
HINTS: GETTING STARTED | I'M STUCK!
Determine the frequency heard by the stationary observer as the train recedes from the observer.
Hz
frequency
=
Transcribed Image Text:PRACTICE IT Use the worked example above to help you solve this problem. A train at a speed of 36.4 m/s sounds it whistle, which has a frequency of 5.06 x 10² Hz. Determine the frequency heard by a stationary observer as the train approaches the observer. The ambient temperature is 21.7°C. Hz EXERCISE HINTS: GETTING STARTED | I'M STUCK! Determine the frequency heard by the stationary observer as the train recedes from the observer. Hz frequency =
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