Question

A wire with mass 55.0 g is stretched so that its ends are tied down at points 100 cm apart. The wire vibrates in its fundamental mode with frequency 65.0 Hz and with an amplitude of 0.800 cm at the antinodes.

a.What is the speed of propagation of transverse waves in the wire?

b.Compute the tension in the wire.

Answer 1

a)
Fundamental node means the wire's vibration is like this:


Since that's 1/2 of a wavelength (which looks like an S), and since the wire is 100cm long, the wavelength is 100 x 2 = 200cm long.

Speed = Frequency x Wavelength
= 65 x 2 = 130ms-1


b)
The equation for tension is
Velocity of wave = square root of (Tension/mass per unit length)
so,
Tension = (Velocity of wave)^2 x mass per unit length

Previously we calculated the velocity as 120ms-1, so

Tension = (130ms-1)^2 x (0.055kg/1m)
= 929.5N