A car moving at 20m/s is sounding its horn as it approaches you. If the actual frequency of the horn is 283 Hz, what frequency will you hear at 25.0 degrees C?
F = ((V + Vr) / (V + Vs)) * Fo.
F = ((343 + 0) / (343 + 20)) * 283,
F = (343 / 363) * 283 = 267.4 Hz.
V = Velocity of sound in air.
Vr = Velocity of the receiver.
Vs = Velocity of the source.
Fo = Transmitted frequency of the source.
F = Frequency received by the receiver.
To determine the frequency that you will hear when the car's horn approaches you, we need to consider the concept of the Doppler effect. The Doppler effect describes the change in frequency that occurs when a source of sound is moving relative to an observer.
The formula for calculating the observed frequency (f') due to the Doppler effect is given by:
f' = (v + v_obs) / (v + v_source) * f_source
Where:
f' is the observed frequency
v is the speed of sound in the medium
v_obs is the velocity of the observer relative to the medium
v_source is the velocity of the source relative to the medium
f_source is the actual frequency of the source
In this case, the car is approaching you at a velocity of 20 m/s, and the actual frequency of the horn is 283 Hz. To calculate the observed frequency, we need to know the speed of sound in the medium and the velocity of the observer relative to the medium.
The speed of sound in air at 25.0 degrees Celsius is approximately 343 m/s. The velocity of the observer (you) relative to the medium is assumed to be zero since you are stationary.
Plugging these values into the Doppler effect formula, we can calculate the observed frequency:
f' = (343 m/s + 0 m/s) / (343 m/s + (-20 m/s)) * 283 Hz
Simplifying the equation:
f' ≈ (343 m/s) / (323 m/s) * 283 Hz
f' ≈ 301.2 Hz
Therefore, you will hear a frequency of approximately 301.2 Hz when the car's horn approaches you at a speed of 20 m/s.