I have a interference of wave question. I really need to understand this question. Please help me!!!!!!?

Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 30cm.

A. What is the wavelength of the sound?

I think the wavelength is 20cm because it has maximum at that point. However, the answer is 80cm. I really don't understand why this answer came up.

B. If the distance between the speakers continues to increase, at what separation will the sound intensity again be a maximum? Well, I got 40cm because of the 20cm of wavelength, but this was also wrong. The answer is 100cm.

Please help me to understand this question why the answer come up with 80cm and 100cm. Thank you so much!!

Answer 1

You do need both pieces of information, since you aren't told that the speakers are in perfect phase.

So, you know that the max occured at 20 cm, and the min (zero) at 30 cm, thus a relative displacement of 10 cm.

That 10 cm moves you from speakers totally in phase to speakers out of phase -- thus 1/2 wavelength.  So, you were correct that 20 cm is the wavelength.  80cm is incorrect -- someone was thinking that 20 cm was the distance from the zero to the peak, which is 1/4 wavelength, and multiplied by 4!  However, this is not the wavelength of the sound coming out of each speaker.  

You are correct on part b as well.  should be 40 cm.