Interference of Waves from Two Sources and Beats

In summary: So you can substitute into the above and solve for u.In summary, the problem involves two loudspeakers emitting 300 Hz notes, with one speaker on the ground and the other on a moving truck. The frequency of the sound waves from the truck can be determined using the beat formula and is lower than the frequency of the speaker on the ground due to the Doppler Effect. The formula for the Doppler Effect can be used to calculate the speed of the truck, with known values for the original frequency, observed frequency and speed of sound.
  • #1
weezer13578
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0

Homework Statement


Two loudspeakers emit 300 Hz notes. One speaker sits on the ground. The other speaker is in the back of a pickup truck. You hear eight beats per second as the truck drives away from you. What is the truck's speed? (Assume that the speed of sound is 343 m/s.)


Homework Equations


These equations could be useful:
change in d= d2-d1, d1 distance is one speaker on the ground, and d2 another speaker on the truck.
Constructive interference: change in d= m*wavelenght, m= 1,2,3,...
Destructive interference: change in d= (m+1/2)* wavelenght, m=1,2,3,...
f(beat)= f1-f2
f(oscillations) = 1/2(f1+f2)

The Attempt at a Solution


I am not sure how to go about this problem. I tried using f(beat) formula but I am stuck. Please help.

Thank you,
 
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  • #2
The beat formula is a good start. That should tell you the frequency of the sound waves from the truck. It should be a lower frequency than the speaker on the ground, due to the motion of the truck.
The reason it is lower is due to the Doppler Effect.
The Doppler formula for the change in frequency due to relative motion should give you the speed of the truck.
Do you know the formula for the Doppler Effect?
 
  • #3
formula for doppler effect is,
change in F = +/- 2*Fo (Vo/V), F is for frequency. how can I use this equation to solve for the speed of the truck, V?
 
  • #4
I don't recognise that formula for the Doppler effect
The observed frequency of the sound from the truck, fo, is
fo = fv/(u+v) when the truck is moving away.
f is original frequency the sound, v is speed of sound, u is speed of truck.
In this formula you know
f, fo and v
The observed frequency we know, from the beats, is less than the original by an amount given by f - fo = fbeat
 

Related to Interference of Waves from Two Sources and Beats

1. What is the concept behind interference of waves from two sources?

The concept behind interference of waves from two sources is based on the principle that when two waves meet, their amplitudes are either added together or subtracted from each other, depending on their phase difference. This results in either constructive interference, where the waves reinforce each other and produce a larger amplitude, or destructive interference, where the waves cancel each other out and produce a smaller amplitude.

2. How does the distance between the two sources affect interference?

The distance between the two sources plays a crucial role in determining the type of interference that occurs. When the sources are closer together, the waves have a shorter distance to travel and the phase difference is smaller, resulting in more pronounced interference patterns. On the other hand, when the sources are farther apart, the waves have a longer distance to travel and the phase difference is larger, resulting in less noticeable interference patterns.

3. What is the difference between constructive and destructive interference?

Constructive interference occurs when the waves from two sources are in phase, meaning their peaks and troughs align and add together to produce a larger amplitude. This results in a brighter or louder signal. Destructive interference, on the other hand, occurs when the waves are out of phase, meaning their peaks and troughs are opposite and cancel each other out, resulting in a smaller amplitude or even complete cancellation of the signal.

4. What is the relationship between beat frequency and the difference in frequency between two sources?

The beat frequency is the difference in frequency between two waves that are interfering with each other. This frequency is equal to the absolute value of the difference in frequency between the two sources. For example, if one source has a frequency of 100 Hz and the other has a frequency of 105 Hz, the beat frequency would be 5 Hz.

5. How is the superposition principle related to interference of waves from two sources?

The superposition principle states that when two or more waves overlap, the resulting wave is the sum of the individual waves. This principle is directly related to interference of waves from two sources because it explains how the waves interact and combine to create either constructive or destructive interference. Without the superposition principle, the concept of interference of waves from two sources would not be possible to understand or predict.

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