Question

Sound of a certain wavelength is coming from within a room and passing through a rectangular door (a "slit"). If the width of the doorway is twice the wavelength of the sound, what is the diffraction angle of the sound leaving the doorway?

Answer 1

The sound waves diffraction angle as it leaves a doorway, which is twice the width of the wavelength, is 30 degrees due to the wave spreading out when passing through the opening.

Step-by-step explanation:

The question pertains to the phenomenon of diffraction of sound waves, which occurs when waves encounter an obstacle or slit that is comparable in size to their wavelength. In this case, we have a sound wave with a wavelength that is half the width of the doorway. Using the diffraction formula for a single slit, sin(θ) = λ / w, where θ is the diffraction angle, λ is the wavelength, and w is the width of the slit, we can calculate the required angle. Because the width is twice the wavelength, we can simplify this to sin(θ) = λ / (2λ) = 1/2, implying that θ is 30 degrees, which is the angle where the first minimum would occur, and thus indicates the spread of the sound wave into the room.