Question

A 21 g string is under 22 N of tension. A pulse travels the length of the string in 60 ms .

1)

How long is the string?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Suppose L is the length of the string.

So, velocity v = L / (60 x 10^-3) = 16.7*L

Here, you can use the following expression to solve the problem -  

v = ?[F / ?]

Where ? is the linear density of the string which equals mass divided by length,

So,  

v = ?[F / (m/L)]

Solved for m :

m = FL / v²

=> 0.021 = (22)(L) / (16.7*L)² = 0.0792 / L
=> L = 0.0792 / 0.021 = 3.77 m

So, length of the string = 3.77 m. = 3.80 m (two significant digits).