Question

The two loudspeakers in the drawing are producing identical sound waves. The waves spread out and overlap at the point P. What is the difference in the two path lengths if point P is at the third sound intensity minimum from the central sound intensity maximum

Answer 1

The difference in path lengths between the two sound waves at the third intensity minimum is three times half the wavelength.

Step-by-step explanation:

In order to find the difference in path lengths, we need to understand the concept of interference in sound waves. When two sound waves from the loudspeakers overlap at point P, they can either interfere constructively or destructively. Constructive interference occurs when the waves are in phase and their crests and troughs align, resulting in a higher sound intensity. Destructive interference occurs when the waves are out of phase and their crests and troughs cancel each other out, resulting in a lower sound intensity.

The maximum sound intensity occurs at the point P when the path length difference between the two waves is an even multiple of the wavelength. The minimum sound intensity occurs at the point P when the path length difference between the two waves is an odd multiple of half the wavelength.

Therefore, if point P is at the third intensity minimum from the central maximum, the path length difference between the two waves is three times half the wavelength.