Question

yolanda is studying two waves. the first wave has an amplitude of 2 m, and the second has an amplitude of 3 m. which statement accurately describes something that yolanda can do as a part of her study? she can use destructive interference to generate a wave with an amplitude of 3.1 m. she can use constructive interference to generate a wave with an amplitude of 1.5 m. she can use destructive interference to generate a wave with an amplitude of 0 m. she can use constructive interference to generate a wave with an amplitude of 3.5 m.

Explanation:

Step1: Recall interference principles

In constructive interference, the amplitude of the resultant wave is the sum of the amplitudes of the individual waves ($A = A_1+A_2$). In destructive interference, the amplitude of the resultant wave is the absolute - value of the difference of the amplitudes of the individual waves ($A=\vert A_1 - A_2\vert$). Given $A_1 = 2m$ and $A_2=3m$.

Step2: Calculate amplitudes for constructive interference

For constructive interference, $A=A_1 + A_2=2 + 3=5m$.

Step3: Calculate amplitudes for destructive interference

For destructive interference, $A=\vert2 - 3\vert=1m$.

Step4: Analyze each option

• Option 1: Destructive interference cannot give an amplitude of $3.1m$ as the maximum amplitude in destructive interference for these two waves is $1m$.
• Option 2: Constructive interference gives an amplitude of $5m$, not $1.5m$.
• Option 3: Destructive interference cannot give an amplitude of $0m$ for these two non - equal amplitude waves.
• Option 4: Constructive interference gives $A = 2+3 = 5m$. But if we consider the general concept of superposition and assume some phase - related adjustments in a more complex scenario where the amplitudes combine in a non - simple linear way for constructive interference, we know that the amplitude of the resultant wave in constructive interference lies between $\vert A_1 - A_2\vert$ and $A_1 + A_2$. A value of $3.5m$ is possible in constructive interference when the waves are not in perfect in - phase or out - of - phase conditions.

Answer:

She can use constructive interference to generate a wave with an amplitude of 3.5 m.