How Does the Doppler Effect Help Determine the Speed of Sound?

In summary, the problem involves a car moving away from a stationary observer, emitting a frequency of 810Hz. The observer hears an apparent frequency of 762Hz. Using the equation f' = f(v/(v+us)), and solving for the speed of sound (v), we get v = f'us/(f-f'), where us is the speed of the source.
  • #1
calculator20
47
0

Homework Statement


Problem: a car is moving away from a stationary observer at 25ms^-1. It emits a frequency of 810Hz and the observer hears an apparent frequency of 762Hz. What is the speed of sound in air at that time?

Homework Equations


The equation for a source moving away is

f' = f(v/(v+us)) where us is speed of source.

The Attempt at a Solution


There are 2 v's and I need just one, I have no idea where to start, please can you help?
 
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  • #2
calculator20 said:
There are 2 v's and I need just one, I have no idea where to start, please can you help?
Of the two speeds, one is given. Just solve for the other.
 
  • #3
Yes I know I have us but there are two v's in the equation and I don't know how to rearrange it to get one v on its own?
 
  • #4
calculator20 said:
Yes I know I have us but there are two v's in the equation and I don't know how to rearrange it to get one v on its own?
Ah, so it's the algebra that's messing you up. First thing to do is get rid of that denominator on the right hand side. How can you do that?
 
  • #5
Multiply by it giving this?

f'v+fus = fv
 
  • #6
calculator20 said:
Multiply by it giving this?

f'v+fus = fv
Almost. That second term on the left should have an f', not an f.
 
  • #7
Oh yes, sorry.

f'v + f'us = fv

I still can't see how I set it down to just one v without somehow cancelling both out along the way?
 
  • #8
calculator20 said:
Oh yes, sorry.

f'v + f'us = fv

I still can't see how I set it down to just one v without somehow cancelling both out along the way?
Keep the term with us where it is, but move all the others to the right. Then you can solve for us.
 
  • #9
But I'm solving for v?
 
  • #10
calculator20 said:
But I'm solving for v?
No, v is the speed of the car. You need to solve for us, which is the speed of sound.
 
  • #11
It's definitely v I need to find. According to my textbook us is the moving source velocity. In the other equation it uses uo as moving observer velocity.
 
  • #12
calculator20 said:
It's definitely v I need to find. According to my textbook us is the moving source velocity. In the other equation it uses uo as moving observer velocity.
You're right! (I must be losing my mind. Sorry about that!)

So just collect all the terms with v in them to one side. Then you can isolate v. [Using ax + bx = (a+b)x]
 
  • #13
f'us=fv-f'v

f'us =v(f-f')

v=f'us/(f-f')

Is that right?
 
  • #14
calculator20 said:
f'us=fv-f'v

f'us =v(f-f')

v=f'us/(f-f')

Is that right?
Perfect!
 
  • #15
Excellent! Thank you so much for your help! :)
 

FAQ: How Does the Doppler Effect Help Determine the Speed of Sound?

1. What is the Doppler effect?

The Doppler effect is a phenomenon that occurs when there is a perceived change in frequency of a wave due to relative motion between the source of the wave and the observer.

2. How does the Doppler effect relate to the speed of sound?

The Doppler effect is commonly observed with sound waves, where the perceived frequency of the sound changes depending on the relative motion between the source of the sound and the listener. This change in frequency can be used to calculate the speed of sound.

3. What factors affect the speed of sound in the Doppler effect?

The speed of sound in the Doppler effect is affected by the relative motion between the source and the observer, the temperature and density of the medium the sound is traveling through, and the direction of the motion.

4. How is the Doppler effect used in real-world applications?

The Doppler effect is used in various real-world applications, such as radar and sonar systems, where it is used to determine the speed and direction of objects. It is also used in medical imaging, such as ultrasound, to create images of internal organs.

5. How is the Doppler effect different from the speed of sound in a stationary medium?

The speed of sound in a stationary medium is the physical speed at which sound waves travel through that medium. The Doppler effect, on the other hand, is a perceived change in frequency due to relative motion between the source and observer. So, while the speed of sound remains constant in a stationary medium, the perceived frequency changes in the Doppler effect depending on the relative motion between the source and observer.

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