F = MA 2011 # 14 (Creating a uniform sound)

[SignaturePF]

Homework Statement

See:
https://aapt.org/physicsteam/2012/upload/exam1-2011-1-3-answers_1.pdf
Number 14

Homework Equations

None that come to mind

The Attempt at a Solution

I think this is a conceptual question where each needs to be more proportionally spread apart because it takes longer to reach the next object after colliding with the one before it.

 

[jedishrfu]

You could work it in reverse imagine you are accelerating upward and use the s=1/2 a t^2

And so every second you are following a t^2 path which if you recall is something like:

1,3,5,7 separation between points which is 1,4,9,16

 

[SignaturePF]

What is a t^2 path - where did you get those numbers (1,3,5,7) from?

 

[jedishrfu]

have you ever plotted y=x^2 with x=0,1,2,3,4 and get y=0,1,4,9,16 then if you take the differences between each point you get 1,3,5,7 right?

 

[SignaturePF]

Yes but how does that relate to this question? And why would you take the difference?

 

[jedishrfu]

Yes but how does that relate to this question? And why would you take the difference?

If you look at the spacing of pointsfor D they follow the 1,3,5,7 sequence or if you number the points from the bottom you get 1,4,9,16 so right there you know you have a parabolic function.

In contrast E tries to fool you as the points are spaced at 1,4,9,16 so might conclude that E is the answer.

and A isn't spaced as a parabola and is backwards
and B is evenly spaced so that's not a parabola
and C is spaced like A but still isn't a parabola

 

[SignaturePF]

And how does a parobolic function signify that the sound is uniform?

 

[jedishrfu]

when things fall the follow s=1/2 a t^2 equation right? and that's a parabolic equation in t.

 

[SignaturePF]

Ok so that makes sense as to why its uniform?

 

[jedishrfu]

so what's left is for you to think about it a bit. You could even do the experiment and listen to the sound.