# Two loudspeakers emit out-of-phase sound waves along the x-axis. The sound has maximum loudness when the speakers are 30 cm apart. The sound becomes quieter as the distance between the speakers is...

Two loudspeakers emit out-of-phase sound waves along the x-axis. The sound has maximum loudness when the speakers are 30 cm apart. The sound becomes quieter as the distance between the speakers is increased, reaching zero at a separation of 60 cm.
If you keep increasing the separation between the speakers, at what separation will you hear the loudest sound again?

quirozd | Certified Educator

90 cm

The best way to visualize this is draw two identical sine waves on two pieces of paper. Flip one over so that the peaks of one line up with the valleys of the other. The two waves would interfere and give you no sound. This represents if both speakers were at zero on the x-axis. Now slide one of the waves forward until peaks line up with peaks. This is where the sound is the loudest. The first instance this happens represents 30cm of separation.

Blue and red overlap and add together having the effect of louder sound. (Constructive interference)

Continue to move until you have peaks line up with valleys again. You should have noticed that you moved half a wavelength in doing so and ended up with double the original separation of 60cm. You can also see that the wavelength of the sound is 60cm. Moving full wavelengths from the first antinode (point of maximum intensity) will get you the subsequent antinodes.

Moving 30cm more causes the sound to destructively interfere such that no sound is heard.

Thus another 30 cm, should have the peaks line up again!