Two speakers are wired to emit identical sounds in unison. The wavelength in air of the sounds is 6 m. Do the sounds interfere constructively or destructively at a point 10 m from both speakers?

Respuesta :

Answer:

Costructively

Explanation:

The condition for constructive interference is:

[tex]|d_1 -d_2| = n \lambda[/tex] (1)

where

d1 is the distance of the point from the 1st source

d2 is the distance of the point from the 2nd source

n is an integer number

[tex]\lambda[/tex] is the wavelength of the wave (in this case, 6 meters)

In this problem, we are considering a point which is 10 m from both speakers, so we have:

[tex]d_1 = 10 m\\d_2 = 10 m\\d_1 - d_2 = 0[/tex]

And so eq.(1) is satisfied when n=0, which is an integer. Therefore, constructive interference occurs.