Chapter 25, Problem 34A

You dip your finger repeatedly into a puddle of water and make waves. What happens to the wavelength if you dip your finger more frequently?

To determine

Wavelength observed by the person when he dips a finger more frequently into the puddle of water.

Answer to Problem 34A

When a person dips his finger into the water more frequently, then wavelength of the water waves decreases.

Explanation of Solution

Introduction: Frequency $\nu$ is inversely proportional to the wavelength $\lambda$ and related to the speed of sound $\text{v}$ as

  $\text{v = }\nu \times \lambda$

When a person dips his finger into the water, then water waves are produced concentrically. If the frequency of dipping into the water increases then more water waves will produce. Since frequency of a disturbance is inversely proportional to the wavelength. Thus, as the frequency increases, so will the wavelength decreases.

Conclusion: Thus, when a person dips his finger into the water more frequently, then wavelength of the water waves decreases.