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

Answer:

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

Explanation:

We have given frequency f = 90 Hz

and velocity of the sound v = 340 m /sec

So wavelength $\lambda =\frac{v}{f}=\frac{340}{90}=3.777m$

Here path difference will be equal to wavelength

So $s_1-s_2=\pm \frac{\lambda }{2}=\pm \frac{3.777}{2}=\pm 1.888$

$s_1-6=\pm 1.888$

$s_1=4.111m,\ 7.888m$

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