Question

Follow these steps to solve this problem: Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 mm apart and are emitting 1700-HzHz sound waves into a room where the speed of sound is 340 m/sm/s . Consider a point 4.0 mm in front of speaker 1, which lies along a line from speaker 1, that is perpendicular to a line between the two speakers. Is this a point of maximum constructive interference, a point of perfect destructive interference, or something in between

Answer 1

The point is neither maximum constructive interference nor perfect destructive interference, the interference is something in between.

Step-by-step explanation:

Given data in the question;

first we find the wavelength of the sound λ

Then we find the path-length difference to the point from the two speakers, and divide it by the wavelength.

wavelength λ = velocity / frequency = 340 m/s / 1700 Hz = 0.2 m

L1 = 4 m

L2 = √(4² +2² ) m

delta L = L2 - L1 = √(4² +2² ) m - 4 m = 0.472 m

x = deltaL / λ

If the result is nearly an integer, the waves reinforce at the point.

If it is nearly an integer + 0.5, the waves interfere destructively at the point.

If it is neither, the point is "something in between".

so we solve for x

x = 0.472 m / 0.2m

x = 2.36

since its not an integer, it is not point maximum constructive interference

delta L = ( 2x + 1 ).λ/2

x = ((2deltaL/λ) - 1)/2

x = (((2×0.472)/0.2) - 1)/2

x = 3.72 / 2

x = 1.86

Here also, it is not an integer, so it is not a point perfect destructive interference.

Therefore, The point is neither maximum constructive interference nor perfect destructive interference, the interference is something in between.