# What is the Maximum Wavelength for Constructive Interference of Sound Waves?

• Cc518
In summary, the maximum possible wavelength of the sound waves emitted by the two in-phase loudspeakers is 2.5 meters.
Cc518

## Homework Statement

Two in-phase loudspeakers, which emit sound in all directions,
are sitting side by side. One of them is moved sideways by 3.0 m,
then forward by 4.0 m. Afterward, constructive interference is
observed 1/4 and 3/4
of the distance between the speakers along the
line that joins them. What is the maximum possible wavelength
of the sound waves?

Δr=r2 - r1 =mλ

## The Attempt at a Solution

The 2 speakers are separated by 5 m, so one speaker is r1= 1/4 x 5m = 1.25m from the point of constructive interference, another speaker is r2=3/4 x 5m = 3.75m from the point of constructive interference.
Δr=r2 - r1 =mλ
= 3.75m-1.25m=2.50m =mλ
So λ=2.5/m
I got λmax=2.5m when m=1
But the answer is 5meters. I don't know why.
Any help is appreciated!

Cc518 said:
I don't know why.
Neither do I.
Maybe it's a typo, should be destructive.

On the other hand, not entirely happy with your answer if we take the question literally. It only says the interference is constructive, not that it is maximally constructive. But that still does not yield 5m.

Sorry, I just assumed that constructive interference means the interference is maximally constructive because I only know how to solve questions when the interference is maximally constructive or maximally destructive.
I am not surprised that the answer is wrong because the textbook has lots of errors.
Thank you for confirming what I did is correct though :)

Cc518 said:
Sorry, I just assumed that constructive interference means the interference is maximally constructive because I only know how to solve questions when the interference is maximally constructive or maximally destructive.
I am not surprised that the answer is wrong because the textbook has lots of errors.
Thank you for confirming what I did is correct though :)
I feel sure they meant maximally con-/de-structive. In fact, if we admit partially constructive the answer to the question is unbounded. For partially destructive, anything just under 10m, I think.

## What is interference of sound waves?

Interference of sound waves is a 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 wave.

## What are the types of interference of sound waves?

The two main types of interference of sound waves are constructive interference, where the resulting wave has a higher amplitude, and destructive interference, where the resulting wave has a lower amplitude.

## How does interference of sound waves occur?

Interference of sound waves occurs when two or more waves meet at the same point in space and time. The resulting wave is determined by the sum of the individual waves at that point.

## What factors affect interference of sound waves?

The factors that affect interference of sound waves include the amplitude and frequency of the individual waves, the distance between the sources of the waves, and the relative phase of the waves.

## What are some common examples of interference of sound waves?

Some common examples of interference of sound waves include the phenomenon of beats in music, the noise-cancelling technology used in headphones, and the interference patterns produced by multiple speakers in a sound system.

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