- #1

- 301

- 15

## Homework Statement

[/B]

I was little bit confused about interference word problem

in an old physics exam. I managed to ace the problem in the exam, by applying a little bit common sense to it, but I feel like I didn't understand the concept of the interference completely.

(Loud)speakers A and B are 3,4m apart from each other and they are sending same-phase signal at 350Hz (ostensibly at the same pace in terms of time synchronosly or however it is said in English)

An observer closes in the distance towards speaker A along the perpendicular line, and that perpendicular line goes through the point A. The perpendicular line is perpendicular to the Line AB which is the distance between speakers A and B.

The observer notices that the sound reacher minimum and maximum values one after the other. The place which corresponds with the first maximum, is located 5m distance apart from point A.

Calculate the speed of sound based on this.

## Homework Equations

## The Attempt at a Solution

I seemed to remember that constructive interference happens

when the sound is at max levels at the observer's location.

Our teacher had given us a little bit confusing formula such as

## \Delta X = ## difference between distances that interfering waves travelled (fair enough)

## \Delta X = n~~*~~ \frac{\lambda}{2} ##

In cases of constructive interference substitute n= {2, 4, 6, 8...}

In cases of destructive interference substitute n= {1, 3, 5, 7...}

well, it is little bit confusing which is the correct n= something? Which n is correct value for each different case and what is the reasoning for it?

One way I did it in the exam was to look at the constructive interference and use some common sense to gauge what is the reasonable velocity. The closest to reasonable speed of sound was calculated when I substituded n= 2

therefore the equation became

## \Delta X = 2* \frac{\lambda}{2} ##

## ~~\leftrightarrow~~ \Delta X = ~~\lambda##

## \leftrightarrow~~ \sqrt{36.56} -5 = \lambda ##

## v= (\sqrt{36.56} -5) * (350) ##

## v= 366.2703 m/s##

using that reasoning you can use the wave equation to calculate ## v= \lambda * f ##