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Anna [14]
3 years ago
15

Problem 1: Two sources emit waves that are coherent, in phase, and have wavelengths of 26.0 m. Do the waves interfere constructi

vely or destructively at an observation point 78.0 m from one source and 143 m from the other source?
2) Repeat problem 1 for observation points are (a) 91.0 m and 221 m and (b) 44.0 m and 135 m from the two sources.
Physics
1 answer:
Anton [14]3 years ago
3 0

1) Destructive interference

The condition for constructive interference to occur is:

\delta = m\lambda (1)

where

\delta =|d_1 -d_2| is the path difference, with

d_1 is the distance of the point from the first source

d_2 is the distance of the point from the second source

m is an integer number

\lambda is the wavelength

In this problem, we have

d_1 = 78.0 m\\d_2 = 143 m\\\lambda=26.0 m

So let's use eq.(1) to see if the resulting m is an integer

\delta =|78.0 m-143 m|=65 m\\m=\frac{\delta }{\lambda}=\frac{65 m}{26.0 m}=2.5

It is not an integer so constructive interference does not occur.

Let's now analyze the condition for destructive interference:

\delta = (m+\frac{1}{2})\lambda (2)

If we apply the same procedure to eq.(2), we find

m=\frac{\delta}{\lambda}-\frac{1}{2}=\frac{65.0 m}{26.0 m}-0.5=2

which is an integer: so, this point is a point of destructive interference.

2) Constructive interference

In this case we have

d_1 = 91.0 m\\d_2 =221.0 m

So the path difference is

\delta =|91.0 m-221.0 m|=130.0 m

Using the condition for constructive interference:

m=\frac{\delta }{\lambda}=\frac{130.0 m}{26.0 m}=5

Which is an integer, so this is a point of constructive interference.

3) Destructive interference

In this case we have

d_1 = 44.0 m\\d_2 =135.0 m

So the path difference is

\delta =|44.0 m-135.0 m|=91.0 m

Using the condition for constructive interference:

m=\frac{\delta }{\lambda}=\frac{91.0 m}{26.0 m}=3.5

This is not an integer, so this is not a point of constructive interference.

So let's use now the condition for destructive interference:

m=\frac{\delta}{\lambda}-\frac{1}{2}=\frac{91.0 m}{26.0 m}-0.5=3

which is an integer: so, this point is a point of destructive interference.

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