Question

A steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.70 cm. (Figure 1) Figure 1 of 1 What stretch of the spring produces a standing wave with two antinodes? Express your answer with the appropriate units.

Answer 1

Answer: 5.80 cm

Step-by-step explanation:

The number of antinodes produced in a standing wave is directly proportional to the length of the wire stretched. In this case, when the spring is stretched by 8.70 cm, it produces three antinodes. Therefore, we can use this proportionality to find the stretch of the spring required to produce two antinodes.

Let x be the required stretch of the spring to produce two antinodes.

Then, we can set up the following proportion:

(number of antinodes) / (length of wire stretched) = constant

3 / 8.70 = 2 / x

Solving for x, we get:

x = (2 * 8.70) / 3

x ≈ 5.80 cm

Therefore, a stretch of 5.80 cm of the spring will produce a standing wave with two antinodes.