When an auditorium has a solid wall, sound waves will tend to perfectly reflect off the wall (i. e. with a 180o phase change). If listening to music, as from an orchestra, the incoming and reflected waves will interfere with each other. For a listener sitting 0.5 m from the wall, what is the lowest frequency which gets suppressed by this interference

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When an auditorium has a solid wall, sound waves will tend to perfectly reflect off the wall (i.e. with a 180o phase change). If listening to music, as from an orchestra, the incoming and reflected waves will interfere with each other. For a listener sitting 0.5 m from the wall, what is the lowest frequency which gets suppressed by this interference? Use vsound=330 m/s.

f = 165 Hz

the lowest frequency which gets suppressed by this interference is 165 Hz

Explanation:

For a reflected wave (out of phase), the path difference between the incoming and reflected wave should be equal to the half integral multiple of wavelength.

r₂ - r₁ = ( m + 1/2) λ/2

r₂ is the distance from the source to observer via reflection

r₁ is distance from source to observer

here r₂ would travel an additional distance of 0.5 m due to reflection that straight approaching wave.

Therefor to have minimum/lowest possible frequency, we say m = 0

we substitute

0.5 = ( 0 + 1/2 ) λ/2

λ = 2m

The frequency would be

f = Vsound / λ

f = 330 / 2

f = 165 Hz

Therefore the lowest frequency which gets suppressed by this interference is 165 Hz

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