The distance a speaker should be placed behind other sound to have an amplitude 1.50 times is 4.523 m.
<h3>What is wavelength?</h3>
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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