You are standing in front of two side by side loudspeakers playing sounds of the same frequency.
Initially you hear no sound. Then one of the speakers is moved away from you. The sound intensity increases until it reaches a maximum when the speakers are 0.75 m apart.
As the speaker continues to move away, the sound starts to decrease. What is the distance between the speakers when the sound intensity is again zero?
The Attempt at a Solution
My solution manual gives this:
Find the wavelength of the sound:
2pi(Δx)/ λ + ϕ0 = m*(2pi) for constructive interference. Δx is the separation between the speakers. Since initially we heard no sound when the speakers were side by side, the speakers are out of phase and ϕ0 = pi. m= 1 because this is the first separation giving constructive interference. Solving for λ gives λ = 1.5 m.
Next use 2pi(Δx)/ λ + ϕ0 = (m + 0.5)*(2pi) for destructive interference. Using m = 1 because this is the second time we're seeing destructive interference, solve for Δx to get Δx = 1.5 m.
What I don't understand is why m = 1 for the first separation giving constructive interference. Shouldn't m = 0 in that case? The formula takes values of m = 0, 1, 2, 3...
m = 1 makes sense for the second time seeing destructive interference, because m would have been zero when the speakers were side by side.