Question

4.One 2.0m long and 4.0g dough rope is held horizontally with one end fixed and the other supporting a 2.0kg mass. Calculate the speed of the transverse waves.

Answer 1

Given that,

A dough rope having length, L = 2.0 m

And mass, M = 4.0 g = 4.0 × 10 ^-3 kg

Rope's one end is fixed and other end is supported by a mass, m' = 2.0 kg

Now, the mass per unit length of rope is

m = M/L , or, m = 4 × 10 ^-3 /2.0

Or, m = 2.0 × 10 ^-3 kg/m

The tension produced by supporting mass within the rope is T= m' × g ( where, g = acceleration due to gravity = 9.81 m/s^{​​​​​​-2}​

Or, T = 2 × 9.81 = 19.62 N

We know that, the speed of the transverse waves is V =

Or, V = 99.045 m/s

So, the speed of the transverse wave is 99.045 m/s (Answer)