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 $A = A_1+A_2$ (maximum) and in destructive interference, the amplitude of the resultant wave is $A=\vert A_1 - A_2\vert$ (minimum), where $A_1 = 2m$ and $A_2=3m$.

Step2: Calculate amplitudes for interference cases

For constructive interference, $A_{max}=A_1 + A_2=2 + 3=5m$ and $A_{min}=\vert A_1 - A_2\vert=\vert2 - 3\vert = 1m$. For destructive interference, $A_{max}=\vert A_1 - A_2\vert=\vert2 - 3\vert=1m$ and $A_{min}=0$ (when waves are out - of - phase by $\pi$).

Step3: Analyze each option

• Option 1: In destructive interference, maximum amplitude is $1m$, can't get $3.1m$.
• Option 2: In constructive interference, minimum non - zero amplitude is $1m$ and maximum is $5m$, can't get $1.5m$.
• Option 3: In destructive interference, when waves are out - of - phase by $\pi$, amplitude can be $0m$.
• Option 4: In constructive interference, maximum amplitude is $5m$, minimum non - zero is $1m$, can't get $3.5m$.

Answer:

She can use destructive interference to generate a wave with an amplitude of 0 m.