   Chapter 14, Problem 42P

Chapter
Section
Textbook Problem

Standing WavesA steel wire in a piano has a length of 0.700 0 m and a mass of 4.300 × 10−3 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (fC = 261.6 Hz on the chromatic musical scale)?

To determine

The tension in the steel wire.

Explanation

Given info: the length of the steel wire is 0.7000m, mass of the steel wire is 4.300×103kg.

The equation for fundamental frequency of the vibration corresponds to the middle of the musical scale.

fc=12LTm/L

Here, fc is the fundamental frequency, L is the string length, T is the string tension, and m is the string mass per unit length.

Rewrite the expression to get T.

Tm/L=2LfcTm/L=4L2fc2T=4Lfc2m

The expression for tension in the steel wire in a piano is,

T=4Lfc2m

Substitute 0

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