Question

A person stands between two speakers driven by the same source. Each speaker produces a tone with a frequency of 200 Hz on a day when the speed of sound is 330 m/s. The person is 1.65 m from one speaker and 4.95 m from the other. What type of interference does the person perceive?

Answer 1

Answer:

The type of interference the person perceives is a Constructive Interference

Explanation:

Before we solve the problem we need to clarify some concepts:  

There are two types of Interference, the Constructive and the Destructive interference  

The Constructive Interference happens if the difference between the waves movement is equal to an even semi-wavelength number

The Destructive Interference is the opposite than the Constructive Interference, it happens if the difference between the waves movement is equal to an odd semi-wavelength number

Taking the above into account let´s proceed to solve the problem.

First, we will need to find how much the wavelength is (we will call it l), we know the frequency f=200Hz, we also know the speed of sound is v=330m/s. We will use the next equation:

$l=v/f$ then we get that $l=1.65m$

In order to find the semi-wavelength we must divide by 2 the previous result, in this case the semi-wavelength will be:  

$l/2=0.825m$

Now, we find the difference between the waves movement, which is the difference between both distances, this difference will be called d and we will find it this way:

$d=4.95m-1.65m$ then d=3.3m

After this, we will do a relation between the distance and the semi-wavelength in order to find what type of interference the person perceives, this way:

$(d)/(l/2)$ then, we have a relation equals to 4. As it´s an even number, we determine the interference is a Constructive Interference