Question

Two speakers are producing identical in-phase sound waves of intensity I and wavelength λ. Choose the phrase that best completes the following sentence: 'If you are a distance r from one speaker and a distance r - λ from the other speaker, then...'

1) you are at a position of constructive interference and the intensity of the sound arriving from the speaker at a distance r - λ is greater than the intensity of the sound from the other speaker.
2) you are at a position of constructive interference and the intensity of the sound arriving from each speaker is the same.
3) you are at a position of destructive interference and you hear no sound at your location.
4) you are at a position of constructive interference and the intensity of the sound arriving from the speaker at a distance r is greater than the intensity of the sound from the other speaker.
5) you are at a position of destructive interference and you hear sound of low intensity.

Answer 1

At the given distances, you are at a position of constructive interference, and the intensity of the sound from each speaker is the same, resulting in a combined intensity that is quadrupled.

Step-by-step explanation:

If you are a distance r from one speaker and a distance r - λ from the other speaker, then you are at a position of constructive interference because the path difference between the two waves is one wavelength (λ). This means that the waves are in phase when they meet at your location, which results in their amplitudes adding together to create a wave with twice the amplitude of the original waves, as per the principle of superposition.

In terms of intensity, which is proportional to the square of the amplitude, perfect constructive interference does not differentiate between the intensities from each individual speaker. Therefore, the second option is correct: 'you are at a position of constructive interference and the intensity of the sound arriving from each speaker is the same.' This results in a combined intensity that is four times the original intensity of one speaker alone.