Fr = (Vs+Vr)/(Vs-Vp) * Fp
Fr = (340+0)/(340-163) * 1730 Hz = 3323
Hz. = Freq. heard by the receiver or
listener.
Fr = (340+0)/(340-163) * 1730 Hz = 3323
Hz. = Freq. heard by the receiver or
listener.
The formula for the frequency of a sound wave observed by a stationary listener due to the Doppler effect is:
f' = (v + vā) / (v + vs) * f
Where:
f' is the observed frequency,
v is the speed of sound,
vā is the velocity of the observer (listener),
vs is the velocity of the source (airplane), and
f is the actual frequency of the source.
In this case:
v = 340 m/s (speed of sound),
vā = 0 m/s (listener is stationary),
vs = -163 m/s (negative because the plane is approaching),
f = 1730 Hz (actual frequency of the source).
Plugging the values into the formula, we can calculate the observed frequency:
f' = (340 + 0) / (340 - 163) * 1730
Simplifying the formula:
f' = 340 / 177 * 1730
Calculating:
f' = 340 / 177 * 1730 ā 3326 Hz
Therefore, the frequency heard by a stationary listener as the plane approaches is approximately 3326 Hz.