Question

Highschool Physics

A train moving at 25 m/s is traveling toward a person waiting at the station. What frequency does the person hear if the train has a horn frequency of 1.0 X 10^3 Hz?

Answer 1

Our givens are
Vs (source) = 25 m/s
Vo (observer) = 0 m/s (just waiting at the station)
f (frequency) = 1x10^3
f’ (observed frequency) = ?

Also let’s assume the speed of sound is V=343 m/s , in most questions it should be a given

Using doppler’s effect

f’ = f * (V ± Vo)/(V ± Vs)

Since the source is approaching the observer, the numerator of the fraction will use a positive sign and the denominator will use a negative sign

f’ = f * (V + Vo)/(V - Vs)

Now we substituted
f’ = (1x10^3) * (343 + 0)/(343-25)
Using a calculator, f’ = 1078.6 Hz
Hope this helps

Answer 2

I don't know the answer, but this is an example

The formula for the Doppler effect is:

�

′

=

�

+

�

�

�

−

�

�

�

f

′

=

v−v

s

v+v

o

f

where

f = 600 Hz is the real frequency of the sound

f' is the apparent frequency

v = 345 m/s is the speed of sound

�

�

=

0

v

o

=0 is the velocity of the observer (zero since it is stationary at the station)

�

�

=

+

25

�

/

�

v

s

=+25m/s is the velocity of the source (the train), moving toward the observer

Substituting into the formula,

�

′

=

345

�

/

�

+

0

345

�

/

�

−

25

�

/

�

(

600

�

�

)

=

646.9

�

�

f

′

=

345m/s−25m/s

345m/s+0

(600Hz)=646.9Hz

(b) 20.1 m/s

In this case, we have

f = 600 Hz is the real frequency

f' = 567 Hz is the apparent frequency

Assuming the observer is still at rest,

�

�

=

0

v

o

=0

so we can re-arrange the Doppler formula to find

�

�

v

s

, the new velocity of the train: