Question

One speaker generates sound waves with amplitude A.

How does the intensity change if we add two more speakers at the same place generating sound waves of the same frequency; one with amplitude 4A in the same phase as the original and the other with the amplitude 2A in the opposite phase?

i) It stays the same.
ii) It is 3x bigger than before.
ii) It is 7x bigger than before.
iv) It is 9x bigger than before.
v) It is 49x bigger than before.

Answer 1

iv) It is 9x bigger than before

Step-by-step explanation:

As the amplitudes of the new speakers add directly with the original one, taking into account the phase that they have, the composed amplitude of the sound wave is as follows:

At = A + 4A -2A = 3 A

The intensity of the wave, assuming it propagates evenly in all directions, is constant at a given distance from the source, and can be expressed as follows:

I = P/A

where P= Power of the wave source, A= Area (for a point source, is equal to the surface area of a sphere of radius r, where is r is the distance to the source along a straight line)

For a sinusoidal wave, the power is proportional to the square of the amplitude, so the intensity is proportional to the square of the amplitude also.

If the amplitude changes increasing three times, the change in intensity will be proportional to the square of the change in amplitude, i.e., it will be 9 times bigger.

So, the statement iv) is the right one.