A train at rest emits a sound at a frequency
of 1089 Hz. An observer in a car travels away
from the sound source at a speed of 30.7 m/s.
What is the frequency heard by the observer? Assume the speed of sound in air to
be 343 m/s.
To find the frequency heard by the observer, we can use the concept of the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave for an observer moving relative to the source of the wave.
The formula for the observed frequency (f') due to the Doppler effect is given by:
f' = (v + vr) / (v + vs) * f
Where:
- f' is the observed frequency
- f is the source frequency (1089 Hz in this case)
- v is the speed of sound in air (343 m/s)
- vr is the velocity of the receiver (observer in the car) relative to the medium (positive if the observer is moving away from the source)
- vs is the velocity of the source (train) relative to the medium (negative if the source is moving away from the observer, which is not the case here)
Given:
- f = 1089 Hz
- v = 343 m/s
- vr = 30.7 m/s
We can substitute these values into the formula to find the observed frequency:
f' = (343 + 30.7) / (343 - 30.7) * 1089 Hz
f' = 373.7 / 312.3 * 1089 Hz
f' ≈ 1299.5 Hz
Therefore, the frequency heard by the observer in the car is approximately 1299.5 Hz.
To find the frequency heard by the observer, we can use the Doppler effect formula:
f' = (v + vo) / (v + vs) * f
Where:
- f' is the frequency heard by the observer
- f is the frequency emitted by the source (train)
- v is the velocity of sound in the medium (343 m/s)
- vo is the velocity of the observer (car)
- vs is the velocity of the source (train)
Given:
- f = 1089 Hz
- v = 343 m/s
- vo = 30.7 m/s (away from the sound source)
- vs = 0 m/s (since the train is at rest)
Plugging in the values into the formula, we get:
f' = (343 + 30.7) / (343 + 0) * 1089
f' = 373.7 / 343 * 1089
f' = 1.09 * 1089
f' = 1187.01 Hz
Therefore, the frequency heard by the observer is approximately 1187.01 Hz.