Question

Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 m apart and are emitting 1700-Hzsound waves into a room where the speed of sound is 340 m/s. Consider a point 4.0 m in front of speaker 1, which lies along a line from speaker 1, that is perpendicular to a line between the two speakers. Is this a point of maximum constructive interference, a point of perfect destructive interference, or something in between?

PART a.Compute the path-length difference?r
part b. What is the wavelength of the sound waves emitted by the speakers?

Answer 1

The point 4.0 m in front of speaker 1 is a point of maximum constructive interference.

Step-by-step explanation:

To determine whether the point 4.0 m in front of speaker 1 is a point of maximum constructive interference, perfect destructive interference, or something in between, we need to compute the path-length difference (Δr) and the wavelength (λ) of the sound waves emitted by the speakers.

a. The path-length difference (Δr) can be calculated using the formula Δr = r2 - r1, where r1 is the distance from the point to speaker 1 and r2 is the distance from the point to speaker 2. Plugging in the values, we get Δr = 4.0 m - 2.0 m = 2.0 m.

b. The wavelength (λ) of the sound waves can be determined using the formula λ = v / f, where v is the speed of sound and f is the frequency of the sound waves. Plugging in the values, we get λ = 340 m/s / 1700 Hz = 0.2 m.

Since the path-length difference (Δr) is equal to one wavelength (λ), the point 4.0 m in front of speaker 1 is a point of maximum constructive interference, where the two sound waves are in phase and reinforce each other.