(a) In which of these scenarios do you hear a higher pitched sound? Explain. (i)

Question

(a) In which of these scenarios do you hear a higher pitched sound? Explain. (i) A train with its horn sounding is stationary and you move directly towards it with a speed v0. (ii) You are stationary and the same train is sounding its horn as it moves directly towards you at speed v0. (b) What is the difference in pitch between the above two scenarios if v0 = 30 m/s , the frequency of the train horn is 800 Hz and the air temperature is 20°C? (c) What is the difference in pitch in (b) if (hypothetically) v0 is one-fifth the speed of sound?

Explanation / Answer

a)

the correct option is (ii)

You are stationary and the same train is sounding its horn as it moves directly towards you at speed v0

becaue,

frequency recieved by the observer is much greter then the in part(i)

b)

frequency, n=800 Hz

observaer speed, vo=30 m/sec

speed of sound V=332+0.61*(20) =334.2 m/sec

if the source is at rest and observer is moving towards the source

n'= n*(v+vo)/v

n'=800*(334.2+30)/(334.2)

n'=871.81 Hz

and

if the observer is at rest and source is moving towards the source

n''= n*v/(v-vs)

n''=800*334.2/(334.2-30)

n''=878.89 Hz

and

difference in pitch is,

dn=878.89-871.81

dn=7.08 Hz

c)

if vo=v/5

then,

n'= n*(v+vo)/v

n'=800*(v+v/5)/(v)

n'=800*(1+1/5)

n'=960 Hz

then,

n''= n*v/(v-v0)

n''=800*v/(v-v/5)

n''=800*1/(1-1/5)

n''=1000 Hz

and

dn=1000-960

=40 Hz

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