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

$v = \sqrt{\frac{T}{\mu}}$

here we will have

$v = \sqrt{\frac{19.6}{0.75\times 10^{-2}}}$

$v = 16.33 m/s$

now we know that frequency is given as

F = 100 Hz

now wavelength is given as

$\lambda = \frac{v}{F}$

$\lambda = \frac{16.33}{100} = 0.16 m$

so wavelength will be 0.16 m