Question

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

Answer 1

7.888m

Step-by-step 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+(1)/(2) )` λ

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

m=0, for minimum destructive interference

Δd=
`(0+(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