A simple pendulum consists of a ball of mass 4.6 kg hanging from a uniform string of mass 0.0601 g and length L. The period of oscillation for the pendulum is 1.43 s. Determine the speed of a transverse wave in the string when the pendulum is stationary and hangs vertically. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.

612.9 m/s

Explanation:

We are given that

Mass=M=4.6 kg

Mass of string=m=0.0601 g=

Length of pendulum=L

Time period=T=1.43 s

We have to determine the speed of transverse wave in the string.

Length of pendulum=

Where

T=Time period

Length of pendulum=

Length of pendulum=L=0.51 m

Mass per unit length=

Tension in the string=

Speed of the wave=

Where T=Tension in the string

Using the formula

Speed of the transverse wave=m/s

Speed of the transverse wave=612.9 m/s

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.