Answer: 30 cm.
Solving
The situation described is that of two sources of sound waves that are separated by some distance. The two waves interfere with each other constructively at some points and destructively at others. When they interfere constructively, the amplitude (and intensity) of the sound wave is greater than when they interfere destructively.
When the speakers are 40 cm apart, the waves that they produce are in phase at some points on the axis, leading to constructive interference and a maximum in the intensity of the sound. As the distance between the speakers is increased beyond 40 cm, the points of constructive interference move farther apart, and the intensity of the sound decreases. When the speakers are 50 cm apart, the waves that they produce are exactly out of phase at some points on the axis, leading to complete destructive interference and a minimum in the intensity of the sound.
If the separation between the speakers continues to increase, the points of constructive interference will move closer together again, and the intensity of the sound will increase. The separation between the speakers at which the intensity of the sound will again be a maximum can be found using the following equation:
d = λ/2 + nλ
where d is the separation between the speakers, λ is the wavelength of the sound wave, and n is an integer that represents the number of half-wavelengths between the speakers.
At the maximum, the separation is an even multiple of half the wavelength, so we can use the formula above with n = 1. The wavelength can be found from the distance between the speakers at the minimum, which is 50 cm, and the distance at the maximum, which is 40 cm:
λ = 2(d_max - d_min) = 20 cm
Substituting λ and n into the formula gives:
d = λ/2 + nλ = 10 cm + 20 cm = 30 cm
Therefore, the sound intensity will be a maximum again when the separation between the speakers is 30 cm.