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

The wave speed of a wave on a string is determined by the tension and linear mass density. The string with the lower linear mass density will have a faster wave speed. Option A is correct.

Step-by-step explanation:

The wave speed of a wave on a string depends on the tension and the linear mass density. The wave speed is given by the formula: speed = √(tension / linear mass density)

In this case, both strings have the same tension, so the wave speed depends only on the linear mass density. The wave speed is inversely proportional to the square root of the linear mass density. Therefore, the string with the lower linear mass density will have a faster wave speed.

Since the thin cooking twine has a lower mass density compared to the heavy rope, you should use the thin cooking twine to achieve the fastest wave speed in your telephone.

Answer 2

a. You should use the thin cooking twine.

Step-by-step explanation:

The velocity of wave on a rope is:

`v=\sqrt{(T)/(\mu)}` (1)

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

`v=\sqrt{(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.