Q. 42

Expert-verifiedFound in: Page 485

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A steel wire is used to stretch the spring of FIGURE P17.42. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0 cm. What stretch of the spring produces a standing wave with two antinodes?

The stretch in the wire is 18cm

The stretch in wire, ∆x= 8 cm =0.08 m The three antinodes are produced, n=3

Let the wavelength is denoted by λThe wavelength of the nth harmonic frequency is given by

Here n=3,

Let the tension in the string is denoted by TThe expression of tension is given by T= k∆xHere, k is the spring constant for wire.Now, the fundamental frequency of the wave is given by

Substitute the values Now, to get two antinodes, n=2, wavelength λ_{2 }is

Now the frequency of the wave in this case is

Compare both the equations ∆x’= 18 cm

Thus the stretch in the wire is 18cm

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