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STALIN [3.7K]
3 years ago
14

n noisy factory environments, it's possible to use a loudspeaker to cancel persistent low-frequency machine noise at the positio

n of one worker. The details of practical systems are complex, but we can present a simple example that gives you the idea. Suppose a machine 6.0 m away from a worker emits a persistent 90 Hz hum. Part A To cancel the sound at the worker's location with a speaker that exactly duplicates the machine's hum, how far from the worker should the speaker be placed
Physics
1 answer:
lys-0071 [83]3 years ago
4 0

Answer:

7.888m

Explanation:

Given:

frequency 'f'= 90Hz

velocity of the sound 'v' = 340 m /sec

The wavelength of the wave is given by,

λ= v/f => 340/90

λ= 3.777m

The destructive interference condition is givn by

Δd= (m+\frac{1}{2}  ) λ

where, m=0,1,2,3,..

m=0, for minimum destructive interference

Δd= (0+\frac{1}{2}  ) x 3.777

Δd=1.888

Therefore, the required distance is

d_f=d_i + Δd => 6 + 1.888

d_f= 7.888m

Thus, So the speaker should be placed at  7.888 m

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