Question

A heavy piece of hanging sculpture is suspended by a 90 cm-long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the tension in the wire?

Answer 1

The tension in the wire is 28.8 N.

Step-by-step explanation:

To find the tension in the wire, we can use the formula for the fundamental frequency of a string:

f = n(v / 2L)

where f is the frequency, n is the harmonic number, v is the speed of sound, and L is the length of the wire.

f = 80 Hz, n = 1, v = ? , and L = 0.9 m .

Since we are given the frequency and the length of the wire, we can solve for the speed of sound:

v = 2fL / n = 2 * 80 * 0.9 / 1 = 144 m/s.

Now, we can use the formula for tension in a string:

T = mLf2

Where T is the tension, m is the mass per unit length of the wire, L is the length of the wire, and f is the frequency.

T = ? , m = 0.005 kg/m , L = 0.9 m, and f = 80 Hz.

T = (0.005 * 0.9 * (80^2)) N = 28.8 N.