Agree or Disagree? Analyzing Wave Amplitudes

[member 731016]

Homework Statement

Please see below

Relevant Equations

Please see below

For this,

The two statements highlighted do not seem to agree. I think the first statement highlighted is referring to A as initial amplitude (which we can denote $A_i$) of the traveling waves before there constructive interference to form antinodes with an amplitude 2A and nodes of an amplitude 0. Where I think the second highlighted statement is referring to when A is the resultant amplitude of standing wave which we can denote $A_f = 2A_i$.

Is my understanding please correct?

Many thanks!

 

[haruspex]

The two statements highlighted do not seem to agree. I think the first statement highlighted is referring to A as initial amplitude (which we can denote $A_i$) of the traveling waves before there constructive interference to form antinodes with an amplitude 2A and nodes of an amplitude 0. Where I think the second highlighted statement is referring to when A is the resultant amplitude of standing wave which we can denote $A_f = 2A_i$.

Is my understanding please correct?

Many thanks!

I believe you are right. There is also the very first sentence of that extract, which also says $\pm A$. I assume A is defined in some preceding text, so both the A references should be 2A.

 

[member 731016]

I believe you are right. There is also the very first sentence of that extract, which also says $\pm A$. I assume A is defined in some preceding text, so both the A references should be 2A.

Great, thank you for your help @haruspex!