Interesting Problem, Not sure where to begin.

[Mbsams]

I need some help getting started on this one:

Sound waves of frequency 582 Hz enter a window 1.3m wide.

The window is in the exact center of one wall of a theater 24m by 12m.

The window is 12m from the opposite wall, along which is a row of seats occupied by people.

The theater is acoustically prepared to prevent the reflection of sound waves, and the speed of sound is 330 m/s.

Two people, on each side of a line directly in front of the window, in the row along the wall hear no sound.

What minimum distance are they from each other?

 

[Andrew Mason]

Sound waves of frequency 582 Hz enter a window 1.3m wide.
The window is in the exact center of one wall of a theater 24m by 12m.
The window is 12m from the opposite wall, along which is a row of seats occupied by people. The theater is acoustically prepared to prevent the reflection of sound waves, and the speed of sound is 330 m/s.

Two people, on each side of a line directly in front of the window, in the row along the wall hear no sound. What minimum distance are they from each other?

This is a 'single slit' diffraction problem. The first minima on the far wall will occur at a point x from the middle of the wall where $x = \lambda L/a$ where a is the slit width and L is the distance from the window to far wall.

I get 10.5 feet.

AM

 

[Mbsams]

Wouldn't that correspond to the first maxima and not minima?

 

[Andrew Mason]

Wouldn't that correspond to the first maxima and not minima?

I think the formula is for the first minima - this is single slit diffraction. You may be using double slit diffraction. I am sure you can check this.

AM