# 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 + 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.