A police car approaches a large wall at 51m/s. Its siren emits a 980 Hz signal.
What is the frequency of the reflected sound observed by the officer?
If we take SOS as 343 m/s
fo = fs [(1+ vo/343)/(1-vs/343)]
in this case vs and vo are the same
To find the frequency of the reflected sound observed by the officer, we need to understand the concept of the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.
In this case, we have a police car moving towards a large wall. As the car approaches the wall, the sound waves emitted by the siren will be compressed, resulting in an increase in frequency. This is known as the "blue shift" of the frequency. Once the sound waves reflect off the wall and travel back towards the officer, they will be stretched, resulting in a decrease in frequency. This is known as the "red shift" of the frequency.
The formula to calculate the observed frequency in terms of the source frequency and the relative velocity between the observer and the source is:
Observed frequency = Source frequency * (Speed of sound + Relative velocity of observer)/(Speed of sound - Relative velocity of source)
In this case, the speed of sound is approximately 343 meters per second (m/s). The relative velocity of the observer is the velocity of the police car, which is 51 m/s. The relative velocity of the source is the velocity of the sound waves, which is the speed of sound.
Using the formula, we can calculate the observed frequency:
Observed frequency = 980 Hz * (343 m/s + 51 m/s)/(343 m/s - 0)
Simplifying this equation gives us:
Observed frequency = 980 Hz * (394 m/s)/(343 m/s)
Calculating this further will give us the observed frequency of the reflected sound observed by the officer.