Question

1)A visitor to a lighthouse wishes to determine the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum, then hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 8.70 s. What is the height of the tower? ___m

2)The speed of a transverse wave on a string is 155 m/s when the string tension is 130 N. To what value must the tension be changed to raise the wave speed to 180 m/s? ___N

Answer 1

1)

here

T = 2 * pie * sqrt(L/g)

8.7 = 2 * 3.14 * sqrt( L / 9.8 )

L = 18.8 m

2)

v = sqrt(T/u) where u is the linear mass density

So u = T/v^2 = 130/155^2 = 5.41 * 10^-3 kg/m

So for v = 180 m/s we have

T = v^2*u = 180^2 * 5.41 * 10^-3 = 175.284 N