Two speakers are 3.0 m apart and play identical tones of frequency 170 Hz. Sam stands directly in front of one speaker at a distance of 4.0 m. Is this a loud spot or a quiet spot? Assume that the speed of sound in air is 340 m/s.

he phase difference is π the destructive interference and the lujar is a still or silent place

Explanation:

This is a sound interference exercise where the amino difference is equal to the phase difference of the sound.

Δr / λ = ΔФ / 2π

Let's find the path difference

r₁ = 4m

r₂ = √ (4² + 3²) = 5 m

Δr = r₂ - r₁

Δr = 5-4 = 1m

Let's find the wavelength of the sound

v = λ f

λ = v / f

λ = 340/170

λ = 2m

Let's find the phase difference between the two waves

ΔФ = Δr 2π / λ

ΔФ = 1 2π / 2

ΔФ = π

Since the phase difference is π the destructive interference and the lujar is a still or silent place