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Q. 42

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 485

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Short Answer

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

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Step by Step Solution

Step 1: Write the given information 

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

Step 2: To determine the stretch in the wire when n=2

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 λ2 is

The stretch in the wire for this case is ∆x’

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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