Question

A recording studio has a soundproof wall, but we need to leave the sliding door open by a small amount because the air conditioner is broken and it is very warm. Suppose sound waves with a wavelength of 50.0 pass through the door. What is the widest we can leave the door open so that everyone on the other side can hear it? (That is, so that there are no quiet spots created by wave interference.)

Answer 1

According to the Huygens-Fresnel principle, when a wave with wavelength λ travels through a slit with a width d, no quiet spots will be created outside the room due to diffraction of waves when:

`d=\lambda`

Therefore, since the wavelength of the sound waves is 50.0cm, the widest we can leave the door open so that everyne on the other side can hear it, is: