Question

Two stereo speakers mounted 4.1 m apart on a wall emit identical in-phase sound waves. you are standing at the opposite wall of the room at a point directly between the two speakers. you walk 1.1 m parallel to the wall, to a location where you first notice that the sound intensity drops to zero. if the wall along which you are walking is 10.7 m from the wall with the speakers, what is the wavelength of the sound waves?

Answer 1

To determine the wavelength of the sound waves, we understand that a path difference of 1.1 m corresponds to a destructive interference position. Since this is the first minimum intensity observed, the path difference is half the wavelength, leading to a calculated wavelength of 2.2 meters.

Step-by-step explanation:

The student's question involves calculating the wavelength of sound waves based on an interference pattern created by two in-phase stereo speakers.

When the student moves to a point where the sound intensity is zero, this indicates a destructive interference, suggesting that the path difference between the two speakers to the point where the student stands is equal to a half-integer multiple of the wavelength (i.e., (n + 1/2)λ, where n is an integer).

Given that the speakers are 4.1 m apart and the student walks 1.1 m parallel to the wall, the path difference between the two sounds waves is 1.1 m. As the sound intensity drops to zero, this point would correspond to the first minimum intensity position (n=0), so the path difference is 1/2λ. Thus, we have:
1/2λ = 1.1 m.
From this, the wavelength λ can be calculated as 2 * 1.1 m = 2.2 m.