Acoustics Question Confusion (Test Q)

[Intel Xeon]

Homework Statement

test q

Relevant Equations

f = 1/t
A + n = L + n^2

This Problem is from a test that has already been attempted.
This problem required some amount of imagination so many of my peers came up with their own unique answers.
It would be very helpful to get to know what the actual solution is. Any amount of assistance will also be helpful.

Question:. A rubber band is stretched across a pencil box and two pencils are inserted on the two ends making a contraption that looks like this

1) If the rubber band is struck will it produce sound? ofc yes

2) Now imagine the length of the pencil box is increased by 10cm
How will the characteristics of sound in this setup (amplitude, pitch, timbre, time period) differ from the characteristics of sound in the previous setup?
The second question is where people had unique answers.

 

[Tom.G]

Too bad you did not have a rubber band in your pocket to run the experiment.

With a rubber band it gets complicated!
Increased length of course lowers the frequency.
Increased tension raises the frequency.
Smaller diameter from stretching (lower mass per unit length)... does something.

Try reading this paper and see what you come up with. (I did only a quick scan and did not spot your particular case.):
https://digitalcommons.linfield.edu/cgi/viewcontent.cgi?article=1035&context=physstud_theses

(above, and many more, found with:
https://www.google.com/search?q=how+string+tension+affect+resonant+frequency)

Have Fun!

Cheers,
Tom

p.s. Please let us know if you find a reasonable answer. My personal opinion is it would depend on the relative sizes of the rubber band and pencil box, and how close to its elastic limit the band is stretched.

 

[haruspex]

Unfortunately, rubber bands are not ideal springs, but I would assume you should take it as being so.
Do you know the equation relating frequency to tension?

 

[Steve4Physics]

I addition to the other answers...

Relevant Equations:: f = 1/t
A + n = L + n^2

I don't recognise the second equation. What are A, n and L?

This Problem is from a test that has already been attempted.

What was the age/level/subject?

This problem required some amount of imagination so many of my peers came up with their own unique answers.
It would be very helpful to get to know what the actual solution is. Any amount of assistance will also be helpful.

Question:. A rubber band is stretched across a pencil box and two pencils are inserted on the two ends making a contraption that looks like this View attachment 322758

1) If the rubber band is struck will it produce sound? ofc yes

2) Now imagine the length of the pencil box is increased by 10cm
How will the characteristics of sound in this setup (amplitude, pitch, timbre, time period) differ from the characteristics of sound in the previous setup?
The second question is where people had unique answers.

What was your answer to the second question?
Why not do the experiment for yourself?

However, IMO it's a poor questionfor a physics test.