A stationary whistle emits a sound of 188 Hz. If passengers in a car hear the whistle with a frequency of 198 Hz, how fast was the car moving? Use 340 m/s for the sound velocity
To calculate the speed of the car, we can use the Doppler effect equation. The equation for the frequency observed by an observer when the source and observer are moving relative to each other is given by:
f observed = f source * (v sound + v observer) / (v sound + v source)
Where:
f observed = observed frequency (198 Hz in this case)
f source = frequency emitted by the source (188 Hz in this case)
v sound = speed of sound (340 m/s in this case)
v observer = velocity of the observer (speed of the car, which we want to find)
v source = velocity of the source (assumed to be zero since the whistle is stationary)
Substituting these values into the equation:
198 Hz = 188 Hz * (340 m/s + v observer) / (340 m/s + 0)
Simplifying the equation:
198 = 188 * (340 + v observer) / 340
Now, we can solve for v observer:
198 * 340 = 188 * (340 + v observer)
67320 = 188 * 340 + 188 * v observer
67320 - 188 * 340 = 188 * v observer
67320 - 64120 = 188 * v observer
3200 = 188 * v observer
v observer = 3200 / 188
v observer ≈ 17.02 m/s
Therefore, the car was moving at approximately 17.02 m/s.