Can you please explain to me why I got a wrong answer on this question?

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

Your answers 20cm and 40cm are correct

Answer 2

Just to give a hint:

Intensity depends on the amplitude, the highest intensity is reached when the waves are in phase(constructive interference; where the trough from one speaker meets the trough of the other and the crests do the same) and at 30cm they cancel out(destructive interference; opposite of constructive intereference)

Answer 3

You have the wavelength wrong.  

If there was only one speaker and a reflector, you get

a quarter wave (max to zero) as 10cm so wavelength is 40cm.

But we have two interfering speakers -

hey this is really tricky!

If they are separated by one complete wavelength (facing each other) they will cancel each other out - at 30cm.

Darn, I can't figure this out either.

Answer 4

Assuming the signal is in perfect synchrony when it leaves the loud speakers, they will cancel when one is 1/4 of wavelength away, and the other 3/4 of wavelength. That way the wave hits maximum from one, when it's going minimum in the other.

Lemmie think.

Answer 5

As stated, your answer are right even though your reasoning is wrong (the wavelength is 20 cm because the difference in separation between constructive and destructive inteference is l/2, and as this is 10cm, l = 20 cm).