Question

In 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 6.0m away from a worker emits a persistent 90Hz hum.

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? Assume a sound speed of 340 m/s.

Answer 1

The speaker should be placed at either 4.111 m or 7.888 m

Step-by-step explanation:

We have given frequency f = 90 Hz

and velocity of the sound v = 340 m /sec

So wavelength
`\lambda =(v)/(f)=(340)/(90)=3.777m`

Here path difference will be equal to wavelength

So
`s_1-s_2=\pm (\lambda )/(2)=\pm (3.777)/(2)=\pm 1.888`

`s_1-6=\pm 1.888`

`s_1=4.111m,\ 7.888m`

So the speaker should be placed at either 4.111 m or 7.888 m