# What Happens to the Wavelength of the Third Harmonic When the Ball Hanging from a Copper Wire Changes?

a. What is the wavelength of the third harmonic for this wire? b. A 500.0 N ball now replaces the original ball. What is the change in the wavelength of the third harmonic caused by replacing the light ball with the heavy one?

**Answer:**a. The wavelength of the third harmonic for the wire can be calculated using the formula λ = 2L/n, where L is the length of the wire and n is the harmonic number. Substituting the values, the wavelength is 0.414 m. b. Replacing the light ball with the heavy one increases the tension in the wire. The change in wavelength can be calculated using the formula Δλ = λ × ΔT/T, where ΔT is the change in tension and T is the initial tension. However, the diameter and length of the wire remain the same, so there is no change in the wavelength of the third harmonic.

## Explanation:

**a. Wavelength of the Third Harmonic:**The third harmonic corresponds to n = 3. Using the formula λ = 2L/n, we can calculate the wavelength as follows: λ = 2(1.24 m) / 3 = 0.414 m.

**b. Change in Wavelength:**The change in wavelength is determined by the change in tension. However, the diameter and length of the wire remain the same, so they do not affect the wavelength. As a result, the change in the tension caused by replacing the ball does not alter the wavelength of the third harmonic. Therefore, there is no change in the wavelength of the third harmonic.