Answer:
The distance we need to walk in other not to hear the speakers for a speaker separation distance of 1 m, while walking in front of one of the speaker is 1.875 meters
Explanation:
The wavelength of the wave is obtained from the formula, v = f × λ
Where;
v = The velocity of the wave = 344 m/s
f = The frequency of the wave = 688 Hz
λ = The wavelength of the wave
λ = v/f = (344 m/s)/(688 Hz) = 1/2 meters
Therefore, for one not to be able to here the speakers, there must be destructive interference and R₁ - R₂ = λ/2 = (1/2)/2 = 1/4 m
Where R₁ and R₂ are the distances from the person to the two speakers respectively
When the distance between the two speakers = 1 meter, we have
R₁ = √(x² + d²), R₂ = √((1 - x)² + d²)
R₁ - R₂ = √(x² + d²) - √((1 - x)² + d²) = 1/4
When we walk from directly in front of one of the speakers, we get;
R₁ - R₂ = √(1 + d²) - √((1 - 1)² + d²) = 1/4
√(1² + d²) - d = 1/4
√(1² + d²) = 1/4 + d
Square both sides gives
1² + d² = 1/16 + d/2 + d²
1² = 1/16 + d/2
d/2 = 1 - 1/16 = 15/16
d = 2 × 15/16 = 15/8
d = 15/8 = 1.875 meters.
