Question

You are making a telephone out of two aluminum cans and some string. You can choose between two types of string: a 2-m length of thin cooking twine or a 2-m length of heavy rope, both used at the same tension.
Which type of string should you use so that you have the fastest wave speed in your telephone?

a. You should use the thin cooking twine.
b. You can choose either because they are the same length and will produce the same wave speed.
c. You should use the heavy rope.

Answer 1

Answer:

a. You should use the thin cooking twine.

Explanation:

The velocity of wave on a rope is:

$v=\sqrt{\frac{T}{\mu}}$ (1)

with T the tension and μ the linear density of the rope that is defined as $\mu=\frac{M}{L}$, so (1) is:

$v=\sqrt{\frac{TL}{M}}$

with M the mass and L the length

Note that if L and T remain constant for bigger M velocity is going to be smaller and vice versa. So, we should chose the lighter rope that is the thin cooking twine to have the fastest wave speed.