Question

A long distance runner is approaching the finish line. There is a band playing music for all the runners who are finishing. If the runner is running at 1.8 m/s and the band is playing music at 991 Hz, what will be the frequency the runner hears as she approaches the band? (v of sound in air = 343 m/s) (1 point)

1019.13 Hz
996.20 Hz
945.71 Hz
978.89 Hz

Answer 1

996.20 Hz

Step-by-step explanation:

This change is frequency happens due to doppler effect

The Doppler effect is the change in frequency of a wave in relation to an observer who is moving relative to the wave source

`f_(observed)=((c+-V_r))/((C+-V_s)) *f_(emmited)\\`

where

C = the propagation speed of waves in the medium;

Vr= is the speed of the receiver relative to the medium,(added to C, if the receiver is moving towards the source, subtracted if the receiver is moving away from the source;

Vs= the speed of the source relative to the medium, added to C, if the source is moving away from the receiver, subtracted if the source is moving towards the receiver.

here the Source is not moving there for Vs=0 and the observer is approaching towards the source. therefore the observed frequency should get higher ie: C+Vr

`f_(observed)=(C+V_r)/(C) *f_(emmited)\\=(343+1.8)/(343)*991\\ =996.2 Hz`