Question

Two loudspeakers, A and B, are driven by the same amplifierand

emit sinusoidal waves in phase. The frequency emitted byeach
speaker is 172 Hz. You are 8.00 m from A. What isthe closest you
can be to B and be at a point of destructiveinterference.

Answer 1

1 m

Step-by-step explanation:

given,

frequency emitted by the speaker,

f = 172 Hz

speed of sound,v = 344 m/s

distance of Point A = 8 m

`wavelength = (speed\ of\ sound)/(frequency)`

`\lambda= (344)/(172)`

λ = 2 m

For destructive interference

`r_a - r_b = (\lambda)/(2)`

`r_b =r_a - (\lambda)/(2)`

`r_b = 8 - (2)/(2)`

`r_b =7 m`

the closest you can be to B and be at a point of destructive interference

= r_a - r_b

= 8 - 7

= 1 m