Question

What happens to the amplitude of the resultant wave when two sound waves with equal amplitude constructively interfere?

Answer 1

Constructive interference means that the waves combine instead of negate. if they are both amplitude x, adding them together would result in 2x, or doubling the amplitude of one of the waves

Answer 2

Answer:

The amplitude of the resultant wave will be twice the amplitude of each wave

Explanation:

- Constructive interference occurs when two waves meet in phase ($\theta=0^{\circ}$, which means that the crest of a wave meets the crest of the other wave: in this case, the amplitude of the resultant wave is the sum of the amplitudes of the single waves

- Destructive interference occurs when the two waves meet in anti-phase ($\theta=180^{\circ}$, which means that the crest of a wave meets the trough of the other wave: in this case, the amplitude of the resultant wave is the difference between the amplitudes of the single wave

In this problem, we have constructive interference between the two waves: this means that the resultant amplitude is the sum of the two waves. Since the two waves have equal amplitude (we can call it A), the resultant amplitude will be

$R= A+A=2 A$

so, twice the amplitude of the single wave.