Doppler effect and beat frequency

In summary, the frequency of speaker A is 207 Hz, while the speed of sound from speaker B is 9.8 m/s so that the listener does not hear beats.
  • #1
Kolika28
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Summary:: Two speakers A and B are at rest, and a listener L stays on the line that connects the two speakers (see picture). The speakers have almost the same frequency. Assume that the speed of sound in air is 340 m/s. When the listener is at rest, he/she hears beats with frequency 6 Hz. The listener is moving towards speaker B with a constant speed of 5 m/s, he/she hears no beat (same frequency from both speakers).

a) What is the frequency of speaker A?

Now the listener is at rest, but the speaker B moves at a constant speed in the same direction that connects A and L. Speed is positive to the right (see the figure), otherwise it is negative.

b) What is the speed of the sound source B (m/s) so that the listener does not hear beats?

1602714043447.png


a) So ##f_beat=abs(f_A-f_B)=6##. Since the listener does not here at beat when moving toward B ##f_A=f_B## here. Then I use the formula for doppler effect:

##f_L=\frac{340 m/s -5 m/s}{340 m/s}*f_A## (1) and ##f_L=\frac{340 m/s+5 m/s}{340}*f_B## (2). I use the fact that ##f_B=f_A-6## and set the equations 1 and 2 equal each other and get that ##f_A=207 Hz##.

b) I don't get the right answer for this problem. I do almost the same like I did in a) :

##f_L=\frac{340 m/s+0}{340 m/s+0}*207 Hz## and ##f_L=\frac{340 m/s+0}{340 m/s +v_B}*(207-6)Hz## and I get that ##v_B=9.8 m/s##. But this is not correct according to my teacher. Does anyone have some tips?
 
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  • #2
Ohh, I see now? Can it be that I forgot a minus sign in the answer?
 
  • #3
Kolika28 said:
Ohh, I see now? Can it be that I forgot a minus sign in the answer?
Certainly the solution to your equation is negative, and the answer should be negative since B has the lower frequency, and will have to move left to sound as high.
 
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  • #4
haruspex said:
Certainly the solution to your equation is negative, and the answer should be negative since B has the lower frequency, and will have to move left to sound as high.
Thank you for your help! :smile:
 
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Related to Doppler effect and beat frequency

1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. This effect is commonly observed in sound waves, where an approaching sound source has a higher frequency and a receding sound source has a lower frequency.

2. How does the Doppler effect affect sound waves?

The Doppler effect causes the perceived frequency of a sound wave to change depending on the relative motion of the source and the observer. This means that the pitch of a sound can appear to be higher or lower depending on whether the source is moving towards or away from the observer.

3. What is the beat frequency?

The beat frequency is the difference between the frequencies of two sound waves that are slightly different in frequency. When these waves are combined, they create a pulsing sound that is heard as a beat. This phenomenon is often used in tuning musical instruments.

4. How is the beat frequency related to the Doppler effect?

The beat frequency is not directly related to the Doppler effect. However, the Doppler effect can affect the frequencies of the two waves that are creating the beat. For example, if one wave is moving towards the observer and the other is moving away, the beat frequency will be higher than if both waves were stationary.

5. What are some real-world applications of the Doppler effect and beat frequency?

The Doppler effect and beat frequency have many practical applications. In medicine, they are used in ultrasound imaging to measure blood flow and in Doppler radar to detect the speed and direction of moving objects. In astronomy, they are used to measure the speed and distance of stars and galaxies. They are also used in music to tune instruments and in police radar guns to measure the speed of vehicles.

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