Problem
Problem
Two identical speakers emit sound waves of frequency 680 Hz uniformly in all directions with a total audio output of 1 mW each. The speed of sound in air is 340 m/s. A point is a distance 2.00 m from one speaker and 3.00 m from the other. a. Find the intensities and from each speaker at point separately. b. If the speakers are driven coherently and in phase, what is the intensity at point ? c. If they are driven coherently but out of phase by , what is the intensity at point ? d. If the speakers are incoherent, what is the intensity at point ?Intuitive explanation
This is a problem about interference of sound waves — you need to figure out whether the two sound sources reinforce or cancel each other at point . The key is to find the path difference (how much farther one wave travels than the other) and compare it to the wavelength. If the path difference is a whole number of wavelengths, the waves arrive in phase and amplify; if it's a half-integer multiple of wavelengths, they cancel. Start by calculating the wavelength from frequency and speed, then use the geometry to find how out-of-step the waves are at .
Intuitive explanation
This is a problem about interference of sound waves — you need to figure out whether the two sound sources reinforce or cancel each other at point . The key is to find the path difference (how much farther one wave travels than the other) and compare it to the wavelength. If the path difference is a whole number of wavelengths, the waves arrive in phase and amplify; if it's a half-integer multiple of wavelengths, they cancel. Start by calculating the wavelength from frequency and speed, then use the geometry to find how out-of-step the waves are at .