Please show work - prompt ratings! You are standing against a wall opposite two
ID: 1949878 • Letter: P
Question
Please show work - prompt ratings!
You are standing against a wall opposite two speakers that are separated by 3.00 m, as shown in the figure. The two speakers begin emitting a 343 - Hz tone in phase. Where along the far wall should you stand so that the sound from the speakers is as soft as possible? Be specific; how far away from a spot centered between the speakers will you be? The far wall is 120. m from the wall that has the speakers. (Assume the walls are good absorbers, and therefore, the contribution of reflections to the perceived sound is negligible.)Explanation / Answer
You are not quite the same distance from each speaker. Some spots are closer to one, some are closer to the other. If the difference in distance is a half a wavelength, they will interfere destructively. They will be out of phase. One will be at the max of the wave while the other is at the minimum. That's the place where the sound is as soft as possible. The path difference is 0 right in the middle at x = 0. At offset x, the path difference is d * x/L where d = separation of the speakers (3.00 m) and L = distance to the far wall (120 m). This is the thing you have to set equal to 1/2 wavelength. x is the only unknown. You'll need the wavelength, which you get by plugging the frequency 343 Hz into v = f * lambda.