Question

For a science experiment, you would like to use the Doppler effect to double the perceived frequency of a harmonica, from the 261.7-Hz tone (middle C) that it emits, to 493.9 Hz (B4 note). Please explain and WRITE answer clearly and will rate.

Part A

Which strategy will accomplish your goal more easily:

move the harmonica

move the observer

Part B

Calculate the speed the harmonica must have in order for a stationary observer to hear 493.9 Hz.

Express your answer to three significant figures and include appropriate units.

Part C

Calculate the speed an observer must have in order to perceive a 493.9-Hz sound from a stationary harmonica that emits sound at 261.7 Hz.

Express your answer to three significant figures and include appropriate units.

Answer 1

observed frequency=actual frequency*(c+vr)/(c+vs)

where c=speed of sound

vr=speed of receiver, positive if receiver is moving towards the source

vs=speed of source, negative if source is moving towards observer

to get double frequency:

if vr=0, then vs will need to be -c/2

if vs=0 , then vr will need to be c.

hence moving the source at half the speed of sound will be easier.

hence moving the harmonica towards the observer will be the easier strategy.

part B:

493.9=261.7*343/(343-vs)

==>vs=161.26 m/s

hence the speed of harmonica has to be 161.26 m/s

in 3 significant figures, answer=1.61*10^2 m/s

part C:

source is stationary.

hence vs=0

then 493.9=261.7*(343+vr)/343

==>vr=303.34 m/s

in 3 significant figures, answer=3.03*10^2 m/s