a jogger runs a 9 m/s and is trailed by a bumblebee moving at 5 m/s and buzzing at a frequency of 270 Hz. what frequency does the jogger hear if the speed of sound in the air is 336 m/s
To determine the frequency that the jogger hears, we need to consider the Doppler effect. The Doppler effect describes the change in frequency of a wave (in this case, sound) due to the relative motion between the source of the wave and the observer.
The formula for the observed frequency (fo) of a wave when there is relative motion between the source and observer is:
fo = (v + vo)/(v + vs) * fs
Where:
fo = observed frequency
v = speed of sound in the medium (336 m/s in this case)
vo = velocity of the observer (jogger)
vs = velocity of the source (bumblebee)
fs = frequency of the source (270 Hz)
In this scenario, the jogger is the observer and the bumblebee is the source. So let's substitute the given values into the formula:
fo = (336 + 9)/(336 + (-5)) * 270
Note that we use -5 m/s for the velocity of the source because it is trailing behind the jogger.
Simplifying the equation:
fo = (345)/(331) * 270
fo ≈ 283.71 Hz
Therefore, the frequency that the jogger hears is approximately 283.71 Hz.