Destructive interference and constructive interference

In summary, two loudspeakers emit sound in phase with a frequency of 266 Hz and are placed 4.0 m apart. An observer at the center (2.0 m from each speaker) experiences constructive interference. The speed of sound is 343 m/s and the lowest frequency for destructive interference is 114 Hz. The next two lowest frequencies are 343 Hz and 572 Hz. To experience destructive interference, the observer must walk a distance of 1.5 m toward either speaker. The condition for destructive interference is when the path difference is equal to half of the wavelength, which in this case is 1.5 m.
  • #1
shawen
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Two loudspeakers are placed facing each 4.0 m apart. The speakers emit sound in phase with a frequency of 266 Hz. An observer at the center (2.0 m from each speaker along the line joining them) experiences constructive interference. The speed of sound is 343 m/s

The lowest frequency at which destructive interference could occur is if 1/2 a wavelength = 1.5 m (the difference between the two)

The speed of sound can be found with the following formula
v = 331 m/s + (0.6 m/s/C)•T
So at 20C you get a speed of 343 m/s.

We know that (1/2)*lambda = 1.5 m, so lambda = 3.0m
The wavelength must be 3 m.

Using the universal wave equation

v = f*lambda
f = v/lambda
f = (343m/s)/(3 m)
= 114 Hz

The lowest freq would be 114 Hz

The next two lowest would be a 3lambda/2 = 1.5 and 5lambda/2 = 1.5

so lambda = 1m and lambda = 0.6m

Those give f = 343 Hz and 572 Hz

i don't know how to find How far toward either speaker must the observer walk to experience destructive interference?
please help me
 
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  • #2
shawen said:
i don't know how to find how far it is

How far what is? (What is "it"?)
 
  • #3
jtbell said:
How far what is? (What is "it"?)
How far toward either speaker must the observer walk to experience destructive interference?
 
  • #4
What is the c
shawen said:
How far toward either speaker must the observer walk to experience destructive interference?
What is the condition for destructive interference? What path difference will give destructive interference?
 
  • #5


To find the distance that the observer must walk towards either speaker to experience destructive interference, we can use the formula for wavelength:

λ = v/f

where λ is the wavelength, v is the speed of sound, and f is the frequency.

In this case, we know that the frequency is 114 Hz and the speed of sound is 343 m/s. Plugging these values into the formula, we get:

λ = (343 m/s) / (114 Hz) = 3 m

This means that the wavelength is 3 meters. Since destructive interference occurs when the difference in distance between the two sources is equal to 1/2 wavelength, the observer must walk towards either speaker until the difference in distance is 1.5 meters. This can be calculated by taking the total distance between the two speakers (4 meters) and subtracting half of the wavelength (1.5 meters).

So, the observer must walk towards either speaker by 4 m - 1.5 m = 2.5 m to experience destructive interference. This would put them at a distance of 0.5 m from one speaker and 3.5 m from the other speaker. At this distance, the sound waves from each speaker would be out of phase, resulting in destructive interference.
 

FAQ: Destructive interference and constructive interference

What is destructive interference?

Destructive interference occurs when two waves of equal frequency and amplitude meet and their crests and troughs align, resulting in cancellation of the wave amplitudes. This leads to a decrease in the overall amplitude of the resulting wave.

What is constructive interference?

Constructive interference occurs when two waves of equal frequency and amplitude meet, but their crests and troughs are offset, resulting in an increase in the overall amplitude of the resulting wave. This happens because the waves combine and reinforce each other.

How does destructive interference affect sound waves?

When destructive interference occurs in sound waves, the resulting sound will have a lower amplitude and may even become inaudible. This can happen when two sound waves with the same frequency and amplitude meet and their crests and troughs align, leading to cancellation of the waves.

How does constructive interference affect light waves?

Constructive interference of light waves can result in brighter and more intense light. This happens when two light waves with the same frequency and amplitude meet, but their crests and troughs are offset, resulting in an increase in the overall amplitude of the resulting wave.

What is the difference between destructive and constructive interference?

The main difference between destructive and constructive interference is the resulting amplitude of the waves. Destructive interference leads to a decrease in amplitude, while constructive interference leads to an increase in amplitude. Additionally, destructive interference occurs when waves align and cancel each other out, while constructive interference occurs when waves combine and reinforce each other.

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