Doppler Effect and the speed of sound

In summary, the speed of the siren can be calculated using the formula S={V[C(V+D)+(D-V)]/[V(-1-C)+D(1-C)]}. The correct answer is obtained by checking the signs in the numerators of the equations for the two different frequencies, with the numerator being negative when the siren is approaching and positive when it is moving away. This leads to a positive speed of +40m/s for the siren.
  • #1
Potatochip911
318
3

Homework Statement


You are moving at a speed of 35m/s and hear a siren coming from behind you and observe the frequency to be 1370 Hz. The siren goes past you and the new frequency heard is 1330 Hz. What is the speed of the siren traveling at? The speed of sound in air is 340m/s.
f1=1370 Hz
f2= 1330 Hz
D=35m/s
V=340m/s

Homework Equations


fl=fo*((V+D)/(V+S))

The Attempt at a Solution


Since the original frequency is not given I decided to make 2 equations with the different frequencies then just divide to eliminate the original frequency.
f1=fo*((V+D)/(V-S)) <-Since the siren is approaching
f1*(V-S)=fo*(V+D)
f2=fo*((V-D)/(V+S)) <-Since the siren is moving away
f2*(V+S)=fo*(V-D)
Dividing the 2nd equation by the first,
[f2*(V+S)]/[f1*(V-S)]=(V-D)/(V+D)
Letting C=f2/f1
C(V+S)(V+D)=(V-D)(V-S)
C(V2+SV+DV+SD)=(V2-DV-SV+SD)
CV2+CSV+CDV+CSD=V2-DV-SV+SD
CV2+CDV+DV-V2=-SV+SD-CSD-CSV
CV(V+D)+V(D-V)=S(-V+D-CD-CV)
S={V[C(V+D)+(D-V)]/[V(-1-C)+D(1-C)]}
Which gives me S=-40m/s which doesn't make any sense, I'm not sure where my mistake is but the correct answer is +40m/s.
 
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  • #2
Check the signs in the numerators of the equations for fi.

When the siren is approaching, you are moving away from the siren (at least relative to the air).
When the siren is moving away, you are approaching the siren (at least relative to the air).
 
  • #3
mfb said:
Check the signs in the numerators of the equations for fi.

When the siren is approaching, you are moving away from the siren (at least relative to the air).
When the siren is moving away, you are approaching the siren (at least relative to the air).
So in f1 are both of the signs negative and in f2 both signs are positive?
 
  • #4
Right.
In both cases, the velocity of the ambulance and your velocity have opposite effects, in one case you have larger numerator and denominator and in the other case both get reduced. Which one is which depends on your choice of the coordinate system.
 

Related to Doppler Effect and the speed of sound

1. How does the Doppler Effect affect the speed of sound?

The Doppler Effect does not directly affect the speed of sound. It is a phenomenon that describes the perceived change in frequency of a sound wave due to the relative motion between the source of the sound and the observer. The actual speed of sound in a medium remains constant.

2. Does the speed of sound change with temperature?

Yes, the speed of sound in a medium is directly proportional to the temperature of the medium. As the temperature increases, the molecules in the medium vibrate faster, resulting in a higher speed of sound.

3. How does the Doppler Effect explain the change in pitch of a siren on a moving ambulance?

The sound waves from the siren of a moving ambulance are compressed in the direction of motion and stretched in the opposite direction due to the Doppler Effect. This results in a higher perceived frequency (pitch) of the sound as the ambulance approaches, and a lower perceived frequency as it moves away.

4. Is the Doppler Effect only applicable to sound waves?

No, the Doppler Effect can also be observed in other types of waves, such as light waves. The change in frequency of light waves due to the relative motion between the source and observer is called the Doppler Shift.

5. How is the speed of sound measured?

The speed of sound can be measured using the formula v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength of the sound wave. It can also be measured using devices such as a stopwatch and a ruler to measure the time and distance traveled by a sound wave.

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