Constructive interference

In summary, two speakers, A and B, are sending out sounds at 400 hz. The question is asking for the distance, x, between speaker A and point P where constructive interference occurs. Using the equations λ = 2ΔL/(2p-1), v = 340 m/s, and f = 400 Hz, the attempt at a solution calculates that the lowest constructive interference occurs at p = 1 and a distance of 0.85 m. However, the nearest node to speaker A may not occur at p = 1.
  • #1
Firben
145
0

Homework Statement



Two speakers A and B, sends out sounds at 400 hz

In what distance x between speaker A and the point P is it constructive interference ?

http://s716.photobucket.com/user/Pitoraq/media/Fys2121_zps9a68fef2.png.html

Homework Equations




λ = 2ΔL/(2p-1),

v = 340 m/s

f = 400 Hz

The Attempt at a Solution



λ = 2ΔL/(2p-1),

λ = 340/400 = 0.85 m <==>

lowest constructive interference p = 1

0.85 m = ΔL <==>

0.85 = y - x, where y = (2.5)^2+x^2=y^2 is the distance between P and B.

Is this right ?
 
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  • #2
That should get you a constructive interference point (node).
I don't think the nearest node to A (i.e., smallest x) occurs for p = 1, though.
 

What is constructive interference?

Constructive interference is a phenomenon that occurs when two or more waves of the same frequency come together and align in a way that results in an increase in amplitude or energy. This can happen with any type of wave, such as light, sound, or water waves.

How does constructive interference differ from destructive interference?

Constructive interference and destructive interference are two opposite phenomena. While constructive interference results in an increase in amplitude, destructive interference results in a decrease or cancellation of amplitude when two waves meet. This is due to the alignment of the waves either reinforcing or canceling each other out.

What causes constructive interference to occur?

Constructive interference occurs when two waves have the same frequency and meet at the same point in space. When this happens, the crests and troughs of the waves align and add together, resulting in a larger amplitude or energy.

How is constructive interference used in practical applications?

Constructive interference is used in many practical applications, such as in noise-cancelling headphones and concert hall acoustics. It is also utilized in medical imaging techniques like ultrasound and MRI, as well as in wireless communication technologies.

Can constructive interference occur with more than two waves?

Yes, constructive interference can occur with any number of waves, as long as they have the same frequency and meet at the same point in space. In fact, multiple waves can constructively interfere to create even larger amplitudes and energies.

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