Determining interference pattern for two loudspeakers

In summary, two loudspeakers emitting 705Hz sound waves into a room, with a listener standing 5m in front and 2m to the side, create a path difference of 1.5 wavelengths, resulting in destructive interference. If the outputs of the loudspeakers were 180 degrees out of phase, there would be a path difference of 5 wavelengths, leading to constructive interference. The values for the path difference and phase difference are close to full destructive and constructive interference, respectively.
  • #1
twinklestar28
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Homework Statement



Two loudspeakers, at the same height are 2m apart and in phase with each other.Both emit 705Hz sound waves into a room. A listener stands 5m in front of the loudspeakers and 2m to one side of the centre.

a) Is the interference pattern at this point constructive,destructive or something in between?

b) How would the situation differ if the outputs of the loudspeakers were 180 ° out of phase?


Homework Equations



Path difference=L1-L2
λ=v/f

The Attempt at a Solution



a) λ=343m/s / 705Hz = 0.486m

Doing Pythagoras on both lengths I get L1=√5^2 +3^2 = √34m
L2=√5^2+1^2 = √26m

path difference=√34-√26, dividing by wavelength gives 1.504409122 so can i round that to say that m=1.5 hence there is destructive interference or do I leave the value like that and say it is something in between?

b) phase difference=∏=mλ=path difference = m=∏-0.7319/ 0.486 = 4.958

Again can I round up to say that m=5 so there is constructive interference since there the number of wavelengths is a whole integer.

A bit confused on the values I am getting and whether I can round, could someone check my answers?
 
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  • #2
twinklestar28 said:

Homework Statement



Two loudspeakers, at the same height are 2m apart and in phase with each other.Both emit 705Hz sound waves into a room. A listener stands 5m in front of the loudspeakers and 2m to one side of the centre.

a) Is the interference pattern at this point constructive,destructive or something in between?

b) How would the situation differ if the outputs of the loudspeakers were 180 ° out of phase?


Homework Equations



Path difference=L1-L2
λ=v/f

The Attempt at a Solution



a) λ=343m/s / 705Hz = 0.486m

Doing Pythagoras on both lengths I get L1=√5^2 +3^2 = √34m
L2=√5^2+1^2 = √26m

path difference=√34-√26, dividing by wavelength gives 1.504409122 so can i round that to say that m=1.5 hence there is destructive interference or do I leave the value like that and say it is something in between?

b) phase difference=∏=mλ=path difference = m=∏-0.7319/ 0.486 = 4.958

Again can I round up to say that m=5 so there is constructive interference since there the number of wavelengths is a whole integer.

A bit confused on the values I am getting and whether I can round, could someone check my answers?

I think you have it right. The differences are less than a percent from full destructive and constructive interference, so I'd go with those answers myself.
 
  • #3
Ok, thanks :)
 

FAQ: Determining interference pattern for two loudspeakers

1. What is an interference pattern?

An interference pattern is a pattern of alternating bright and dark regions that is created when two or more waves overlap or interfere with each other. This can occur when two loudspeakers emit sound waves at the same frequency.

2. How do you determine an interference pattern for two loudspeakers?

To determine an interference pattern for two loudspeakers, you will need to measure the distance between the two speakers and the distance from each speaker to a specific point where you want to observe the interference pattern. You will also need to know the frequency of the sound waves being emitted from the speakers.

3. What factors can affect the interference pattern for two loudspeakers?

The distance between the two loudspeakers, the distance from the speakers to the observation point, and the frequency of the sound waves can all affect the interference pattern. Additionally, any obstructions or barriers between the speakers and the observation point can also influence the pattern.

4. How can the interference pattern be manipulated?

The interference pattern can be manipulated by changing the distance between the two loudspeakers, the distance from the speakers to the observation point, or the frequency of the sound waves. Additionally, changing the position or orientation of the speakers can also alter the interference pattern.

5. What is the significance of studying interference patterns in relation to loudspeakers?

Studying interference patterns in relation to loudspeakers can help us understand how sound waves interact with each other and how they can be manipulated to create specific patterns and effects. This knowledge can be applied in various fields such as audio engineering, acoustics, and even in the design and placement of speakers in concert venues or auditoriums.

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