Question

The end of a horizontal rope is attatched to a prong of an electricity driven tuning fork that vibrates at 100hz. The other end passes over a pulley and supports a 2-kg mass. The linear mass of the rope is 0.75kg/m. What is the wavelength of a transverse wave on the rope?

A. 0.25m
B. 0.16m
C. 0.12m
D. 1.2m

Answer 1

here since string is attached with a mass of 2 kg

so here tension force in the rope is given as

`T = mg`

here we will have

`T = 2(9.8) = 19.6 N`

now we will have speed of wave given as

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

here we will have

`v = \sqrt{(19.6)/(0.75* 10^(-2))}`

`v = 16.33 m/s`

now we know that frequency is given as

F = 100 Hz

now wavelength is given as

`\lambda = (v)/(F)`

`\lambda = (16.33)/(100) = 0.16 m`

so wavelength will be 0.16 m