An airplane traveling at v = 163 m/s emits a sound of frequency 1730 Hz. At what frequency does a stationary listener hear the sound as the plane approaches? Use 340 m/s for the speed of the sound and answer in Hz.
Fr = (Vs+Vr)/(Vs-Vp) * Fp
Fr = (340+0)/(340-163) * 1730 Hz = 3323
Hz. = Freq. heard by the receiver or
listener.
To find the frequency heard by a stationary listener as the plane approaches, we need to consider the effect of the Doppler effect. The Doppler effect describes the change in frequency of a wave when there is relative motion between the source of the wave and the observer.
The formula for the frequency of a sound wave observed by a stationary listener due to the Doppler effect is:
f' = (v + v₀) / (v + vs) * f
Where:
f' is the observed frequency,
v is the speed of sound,
v₀ 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),
v₀ = 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 ≈ 3326 Hz
Therefore, the frequency heard by a stationary listener as the plane approaches is approximately 3326 Hz.