How do different path differences affect interference in sound waves?

In summary: I solved part a using just nλ/2 and not n+1/2 λ or n-1/2 λ. For part b, I would have simply just done it as xa-xb= 2x-L = lλ so x = L/2 + l/2 λ.
  • #1
Taniaz
364
1

Homework Statement


Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is L = 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is f = 206 Hz. Consider point P between the speakers and along the line connecting them, a distance x to the right of speaker A. Both speakers emit sound waves that travel directly from the speaker to point P. a) For what values of x will destructive interference occur at point P? b) For what values of x will constructive interference occur at point P?

Homework Equations


Path differences for destructive (n + 1/2 λ) and constructive interference.(n λ)

The Attempt at a Solution


For part a) xa-xb = x-(L-x) = 2x-L = (2l -1) λ/ 2, where l is an integer and then they got x = L/2 + (2l - 1)λ / 4
I don't understand how they got (2l -1) λ / 2 and x = L/2 + (2l - 1)λ / 4
For b) xa-xb= 2x-L = lλ so x = L/2 + l/2 λ

For a I would have simply just done it as 2x-L = λ/2 so x = L/2 + λ/4
 
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  • #2
Ok is the destructive interference equation n+1/2 λ or n - 1/2 λ. If it's the latter then the question makes sense but then are both their and my answers correct?
 
  • #3
Tip: Draw a sine wave. Then redraw it twice below, once shifted +1/2λ and once -1/2λ.
 
  • #4
They both interfere destructively so it would be +/- 1/2 λ?
 
  • #5
Some people use n+1/2λ and in places they use n-1/2 λ?
 
  • #6
When solving this question: Two identical loudspeakers are located at points A and B, 2.00 m apart. The loudspeakers are driven by the same amplifier and produce sound waves with a frequency of 784 Hz. Take the speed of sound in air to be A small microphone is moved out from point B along a line perpendicular to the line connecting A and B (line BC in Fig. P16.70). (a) At what distances from B will there be destructive interference? (b) At what distances from B will there be constructive interference? (c) If the frequency is made low enough, there will be no positions along the line BC at which destructive interference occurs. How low must the frequency be for this to be the case?

I solved part a using just nλ/2 and not n+1/2 λ or n-1/2 λ

Not sure what to do with part c as to how low the frequency must be.
 
  • #7
The lower the frequency the longer the wavelength. For destructive interference the path difference must be at least one half wavelength.
 
  • #8
Thank you.

Some people use nλ/2 or
n+1/2λ and in other places they use n-1/2 λ? What's the difference?
 

Related to How do different path differences affect interference in sound waves?

What is interference of sound?

Interference of sound refers to the phenomenon where two or more sound waves interact with each other, resulting in a change in the overall amplitude and/or frequency of the resulting sound.

What causes interference of sound?

Interference of sound is caused by the superposition of sound waves. When two or more sound waves meet, they combine and their individual amplitudes and frequencies add together, resulting in a new sound wave with a different amplitude and frequency.

What are the types of interference of sound?

There are two types of interference of sound: constructive interference and destructive interference. Constructive interference occurs when two sound waves with similar frequencies and amplitudes meet, resulting in a sound wave with a higher amplitude. Destructive interference occurs when two sound waves with opposite frequencies and/or amplitudes meet, resulting in a sound wave with a lower amplitude, or even complete cancellation of the sound.

How does interference of sound affect the quality of sound?

Interference of sound can either enhance or diminish the quality of sound. If constructive interference occurs, the sound will have a higher amplitude and therefore be perceived as louder and stronger. However, if destructive interference occurs, the sound can be partially or completely cancelled, resulting in a decrease in quality or even silence.

What are some real-world examples of interference of sound?

Some common examples of interference of sound include echoes in a large room or canyon, noise-cancelling headphones, and the beats heard when two musical instruments play slightly out of tune with each other. Interference of sound is also the basis for many acoustic engineering techniques, such as noise reduction and sound amplification.

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