The 17500 Hz whine of the turbines in the jet engines of an aircraft moving with speed 280 m/s is heard at what frequency by the pilot of a second craft trying to overtake the first at a speed of 380 m/s?
F = ((V+Vr)/(V+Vs))*Fs,
V = 343 m/s = Speed of sound in air.
Vr = 380 m/s = Speed of receiver.
Vs = 280 m/s = Speed of source.
Fs = 17,500 Hz. = Frequency of source.
F = 20,309 Hz.
Plug-in the given values to verify results.
f
To solve this question, we need to consider the Doppler effect. The Doppler effect is the apparent change in frequency of a sound wave or light wave caused by the relative motion between the source and the observer.
The formula for calculating the observed frequency is given by:
f' = f * (v + v0) / (v + vs)
Where:
f' is the observed frequency,
f is the source frequency (17500 Hz in this case),
v is the speed of sound (approximately 343 m/s),
v0 is the speed of the observer (380 m/s), and
vs is the speed of the source (280 m/s).
Now let's substitute the values into the formula:
f' = 17500 * (343 + 380) / (343 + (-280))
Simplifying the equation:
f' = 17500 * 723 / 63
f' = 200817 Hz
Therefore, the frequency heard by the pilot of the second aircraft is approximately 200817 Hz.