Two loudspeakers 42.0 m apart and facing each other emit identical 115 Hz sinusoidal sound waves in a room where the sound speed

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Two loudspeakers 42.0 m apart and facing each other emit identical 115 Hz sinusoidal sound waves in a room where the sound speed

is 345 m/s. Susan is walking along a line between the speakers. As she walks, she finds herself moving through loud and quiet spots. If Susan stands 19.5 m from one speaker, is she standing at a quiet spot or a loud spot?

Physics

1 answer:

ValentinkaMS [3.4K] · Answer 1 · 2026-03-02T18:17:38+03:00

Answer:

She will be located in a loud area.

Explanation:

To evaluate whether Susan is situated in a quiet or loud area, we must first ascertain the difference in the sound waves reaching her from the two speakers.

If we refer to d₁ as the distance to speaker A, which measures 19.5 m, then d₂ to the other speaker is calculated as follows:

d₂ = 42.0 m - 19.5 m = 22.5 m

This reveals that the path difference between both speakers is:

d = d₂-d₁ = 22.5 m -19.5 m = 3.0 m

Next, we relate this distance to the sound wave's wavelength; for constructive interference, the path difference must equal an even multiple of half the wavelength:

d = (2n)*(λ/2)

To determine λ, we know that for any wave, the relationship between speed, frequency, and wavelength holds:

v = λ*f

λ = v/f = 345 m/s / 115 (1/s) = 3.0 m.

Since the difference between the distances to Susan from both speakers corresponds exactly to one wavelength, this indicates that both waves arrive at the same phase, resulting in constructive interference, thus labeling it as a loud area.

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