Location of the particles when 1.5 periods of a sound wave have passed

[ellieee]

Homework Statement

draw the positions of the particles for t=3.0s. particles take 2s to complete one full oscillation.

Relevant Equations

compressions and rarefactions

qn iv.
I understand that when 1.5 periods pass, every compression will become rarefaction, and every rarefaction will become compression(someone please correct if wrong) but the answer key shows something else.
I'm interpreting the answer key drawing to be 1 compression and 4 rarefactions? someone pls correct me if I am wrong thank you:)

 

[Steve4Physics]

I’m impressed by the way you have managed to manipulate the first image into a wave-shape, to match the topic. Well done!

Call the 9 particles (left-to-right) P1, P2, … P8 and P9.
This means P5 is what the question just calls ‘P’.

In your answer key diagram, the bottom row shows the t=0 positions of all 9 particles. But the top row (for t=3s) shows only 7 of the 9 particles.

At t=0:
P1, P2 and P3 form a compression;
P4, P5 and P6 form a rarefaction;
P7, P8 and P9 form a compression.

At t=3s (as shown on top row of answer key diagram):
P2 and P3 form part of a rarefaction (P1 is too far left to show on the diagram);
P4, P5 and P6 form a compression;
P7 and P8 form part of a rarefaction (P9 is too far right to show on the diagram).

Edit. Typo' corrected.

 

[ellieee]

but what's their reason for not showing P9 and P1? if we still draw them out, is it "wrong"?

I’m impressed by the way you have managed to manipulate the first image into a wave-shape, to match the topic. Well done!

Call the 9 particles (left-to-right) P1, P2, … P8 and P9.
This means P5 is what the question just calls ‘P’.

In your answer key diagram, the bottom row shows the t=0 positions of all 9 particles. But the top row (for t=3s) shows only 7 of the 9 particles.

At t=0:
P1, P2 and P3 form a compression;
P4, P5 and P6 form a rarefaction;
P7, P8 and P9 form a compression.

At t=3s (as shown on top row of answer key diagram):
P2 and P3 form part of a rarefaction (P1 is too far left to show on the diagram);
P4, P5 and P6 form a compression;
P7 and P8 form part of a rarefaction (P9 is too far right to show on the diagram).

Edit. Typo' corrected.

 

[Steve4Physics]

but what's their reason for not showing P9 and P1? if we still draw them out, is it "wrong"?

I'd guess that including P1 and P9 would make the diagram too wide to fit into the available printing-width.

Ideally, whoever prepared the diagrams should have made them smaller (less wide); then all 9 particles could be included in both the t=0 and t=3s diagrams.

It's not wrong to draw all 9 particles, providing they are in the correct positions. If there were enough space, that's what I'd do.