Does Constructive Interference Double Sound Intensity at Source Point in Water?

[GT1]

If two sound sources (A, B) are placed in a water tank and emit sound waves at the same frequency, phase and amplitude, if I measure the sound intensity at point A, will the detected signal will be ~double than the emitted signal of each sound source?
I think that the answer is yes because of the constructive interference between the sound sources, but what is not clear to me is why- all the sound waves that are emitted from source A have momentum in the direction of point B, if the net movement of the water molecules is in the direction of point B, how do they interact with a detector at point A (they only move away from it..)
See the attached drawing.

 

[Claude Bile]

The intensity at "A" will be infinite (as you have posed the problem) because you have a point source of finite power localised over an infinitesimal area/volume.

I think question you were trying to get at is "What is the intensity at the midpoint of A and B?". The answer, as you rightly allude to; is zero, because the interference between A and B is destructive if the waves are longitudinal.

Claude.

 

[GT1]

The intensity at "A" will be infinite (as you have posed the problem) because you have a point source of finite power localised over an infinitesimal area/volume.

I think question you were trying to get at is "What is the intensity at the midpoint of A and B?". The answer, as you rightly allude to; is zero, because the interference between A and B is destructive if the waves are longitudinal.

Claude.

I'm asking about a real world problem - the sound sources and the detector have finite dimensions.
What is the sound intensity very close to point A? Why?

 

[nasu]

In a real problem, you will need to use parameters that you measure in the real setup.
The answer will depend on the phase difference between the two waves at the point of interest.
"A point near the source" is not a specific location.
And the phase difference will depend on the wavelength of the sound, so even for the same point, the answer depends on both specific location and wavelength.

The particles in the medium do not move "forward" but oscillate back and forth. If the oscillations are in phase, the amplitude is larger and you have a maximum of interference. The oscillations may not be along the same direction, true.

 

[sardar]

Yes, you are correct. When two sound sources emit waves at the same frequency, phase, and amplitude, they will experience constructive interference. This means that the peaks and troughs of the waves will align, resulting in a larger amplitude at certain points in the water tank. This can lead to a doubling of the sound intensity at certain points, including point A.

This phenomenon can be explained by the superposition principle, which states that when two or more waves overlap, the resulting wave is the sum of the individual waves. In this case, the waves from sources A and B are overlapping and adding together, resulting in a larger wave at certain points.

As for your question about how the waves interact with a detector at point A, it is important to remember that sound waves are mechanical waves that travel through a medium, in this case water. The water molecules themselves do not carry the sound, but rather the disturbance of the molecules creates the sound wave. So, even though the net movement of the water molecules may be towards point B, the sound wave can still travel in all directions, including towards point A.

In summary, the sound intensity at point A will be approximately double the emitted signal of each sound source due to constructive interference, where the waves from sources A and B add together to create a larger wave.