A 5000-Hz car horn is blasted while the car is moving at 35.0 m/s toward a dazed physics student (stationary). What is the frequency of the horn heard by the student. Assume the temperature is 0°C
Use the Doppler equation for a moving source and assume speed of sound is 343m/s.
To determine the frequency of the car horn heard by the physics student, we need to apply the Doppler effect formula. The Doppler effect is the change in frequency of a wave (sound or light) due to the relative motion between the source of the wave and the observer.
The formula for the apparent frequency of a sound wave, as observed by an observer moving towards or away from the source, is given by:
f' = f((v + vo) / (v + vs))
Where:
f' is the apparent frequency observed by the observer
f is the actual frequency of the source
v is the speed of sound in air (approximately 343 m/s at 0°C)
vo is the speed of the observer (student)
vs is the speed of the source (car)
In this case, the car is moving towards the student at a speed of 35.0 m/s, and the frequency of the car horn is 5000 Hz. The speed of sound in air at 0°C is 343 m/s.
Using the formula mentioned above, we can plug in the given values:
f' = 5000 ((343 + 0) / (343 + 35.0))
= 5000 (343 / 378)
= 4530.687 Hz (rounded to four decimal places)
Therefore, the frequency of the horn heard by the student is approximately 4530.687 Hz.