Beat frequency and Doppler shift

In summary: In order to "hear no beat" or have an "inverse beat frequency", two conditions must be met:The speeds of the two objects must be the same.The frequencies of the two objects must be the same.
  • #1
dawn-
2
0
Homework Statement
Angharad stands midway between two speakers with frequencies 258 Hz and 262 Hz. The speed of sound in the air is 340 m/s. If Angharad does not want to hear beats, how fast and in which direction should she run so that the frequencies she hears from the two speakers are the same? What is this frequency she hears?
Relevant Equations
λ=vT
|f1-f2|= fb
(f1+f2)/2 = fc
(v±vo / v±vs)(f) = fo
where v = speed of wave, vo = speed of observer, vs = speed of source, f = frequency of wave, fo = frequency observed
I found the beat frequency to be 4 Hz and the carrier frequency to be 260 Hz, but I'm not sure how to apply them to the solution/integrate the doppler and beat frequency equations?
 
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  • #2
dawn- said:
I found the beat frequency to be 4 Hz and the carrier frequency to be 260 Hz, but I'm not sure how to apply them to the solution/integrate the doppler and beat frequency equations?
Seems to me there are infinitely many solutions if able to run in any direction, so assume it is directly towards one speaker. If the running speed is v and the speed of sound is c, what two frequencies will be heard?
 
  • #3
haruspex said:
Seems to me there are infinitely many solutions if able to run in any direction, so assume it is directly towards one speaker. If the running speed is v and the speed of sound is c, what two frequencies will be heard?
I'm still real lost... I first thought "hearing no beat" means I should set the beat frequency to zero because f1 needs to equal f2 for that to be true, but that doesn't make any sense if I use that to try and solve for running speed..? What conditions need to be met in order to hear no beat?
 
  • #4
dawn- said:
hearing no beat" means I should set the beat frequency to zero because f1 needs to equal f2 for that to be true, but that doesn't make any sense if I use that to try and solve for running speed..
Why doesn't it make sense? Anyway, please put that aside for the moment and try to answer the question I asked in post #2.
dawn- said:
What conditions need to be met in order to hear no beat?
You are told that:
"so that the frequencies she hears from the two speakers are the same"
 

FAQ: Beat frequency and Doppler shift

What is beat frequency?

Beat frequency is the difference between the frequencies of two sound waves that are interfering with each other. It is perceived as a pulsing sound that occurs when two waves with slightly different frequencies are played together.

How does beat frequency relate to Doppler shift?

Beat frequency and Doppler shift are both phenomena that occur when there is a difference in frequency between two sound waves. However, beat frequency is caused by the interference of two waves, while Doppler shift is caused by the relative motion of the source and observer.

What factors affect beat frequency and Doppler shift?

The factors that affect beat frequency and Doppler shift include the frequencies of the two waves, the relative motion between the source and observer, and the speed of sound in the medium.

How is beat frequency and Doppler shift used in science?

Beat frequency and Doppler shift are used in various scientific fields, such as astronomy, acoustics, and medical imaging. They can be used to measure the motion of objects, study the structure of distant objects, and diagnose medical conditions.

Can beat frequency and Doppler shift be heard or observed by humans?

Yes, both beat frequency and Doppler shift can be heard or observed by humans. Beat frequency can be heard as a pulsing sound, while Doppler shift can be observed as a change in the pitch of a sound wave or the color of a light wave.

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