Question

a steel piano wire 1.2 m long is designed to have a natural frequency of 280 hz when its tension is 620 n. assuming the wire is pure steel, what should its diameter be? the density of steel is 7860 kg/m3.

Answer 1

The diameter of the steel piano wire should be approximately 0.022 meters.

Step-by-step explanation:

To determine the diameter of the steel piano wire, we can use the formula for the natural frequency of a wire:

f = (1/2L) √(T/μ)

Where:
f is the natural frequency
L is the length of the wire
T is the tension in the wire
μ is the linear mass density of the wire

First, rearrange the formula to solve for the diameter:

d = √(4μL2f2/T2)

Substitute the given values into the equation to find the diameter:

d = √(4 * 7860 * (1.2)^2 * (280)^2 / 620^2)

= 0.022 m

Therefore, the diameter of the steel piano wire should be approximately 0.022 meters.