The distance a speaker should be placed behind other sound to have an amplitude 1.50 times is 4.523 m.
The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.
Wavelength λ = v/f
Two in-phase loudspeakers emit identical 1000 Hz sound waves along the x-axis.
λ = 343 m/s /1000 Hz
λ = 0.343 m
Distance, one should speaker be placed behind the other for the sound to have an amplitude 1.50 times that of each speaker alone.
The amplitude of the waveform due to waves,
A = 2a cos (ΔΦ/2)
ΔΦ = 2π x Δx/λ
So, A = 2a cos (π x Δx/λ)
Substitute the values, we get
1.5a = 2a cos (3.14 x Δx/ 0.343)
Δx = 4.523 m
Thus, the distance is 4.523 m.
Learn more about wavelength.
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