Problem 1: two sources emit waves that are coherent, in phase, and have wavelengths of 26.0 m. do the waves interfere constructively 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.

1) Destructive interference

The condition for constructive interference to occur is:

(1)

where

is the path difference, with

is the distance of the point from the first source

is the distance of the point from the second source

m is an integer number

is the wavelength

In this problem, we have

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

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

Let's now analyze the condition for destructive interference:

(2)

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

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

2) Constructive interference

In this case we have

So the path difference is

Using the condition for constructive interference:

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

3) Destructive interference

In this case we have

So the path difference is

Using the condition for constructive interference:

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

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

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

f=ma newton's second law 7x8=56n

hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )