A new car is advertised as having anti-noise technology. The manufacturer claims that inside the car any sound on negated. Evaluate the possibility of such a claim. What would have to be created to cause destructive interference with any sound in the car? Do you believe the manufacturers claim is correct?

I guess you mean that any sound coming from outside is negated, first, this would mean that you can not hear some signals that may help you to avoid accidents, so you do not want this technology.

Now, let's see if it is possible.

Suppose you have a soundwave approaching the car, the car needs to cancel the soundwaves as the soundwaves approach to the surface, to do it, you need to create another wave that is equal in amplitude, but with a change of phase of pi.

in order to do this, the car must be able to "analyze" the coming soundwave and instantly create another one to cancel it. Suppose that the sound is canceled. now if the sound changes, the car must be able to also change the sound that the car is producing, this instantaneous change is one of the problems.

Another problem is that, as you know, the sound propagates as spherical waves, this means that the wavefront of a wave produced far away will have a bigger radius than the soundwave produced by the car, then we never will have a situation where the wavefront is canceled: This means that we only can cancellate the sound in some areas of the car, and we still will have some sound in other parts of the car.

Another way to isolate the car is with isolating panels, those panels absorb the sound and transmit a very little amount of it (those panels are used in recording studios, for example). With enough of those you can cancel almost all the sound coming from the outside, but to do this you will need a big car because the amount of isolating material needed is a lot.  

We can conclude that the manufacturers claim is not correct.

this is poiselle's equation from fluid mechanic in physics. mech eng

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