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Chapter 14: Problem 15

Ripples in a shallow puddle propagate at \(34 \mathrm{cm} / \mathrm{s}\). If the wave frequency is \(5.2 \mathrm{Hz}\), find (a) the period and (b) the wavelength.

Short Answer

Expert verified
The period is approximately 192 milliseconds and the wavelength is approximately 0.065 meter.

Step by step solution

01

Calculate the wave period

Using the relationship \(T = 1/f\), where \(T\) is the wave period and \(f\) is the wave frequency. Given the frequency \(f = 5.2 \mathrm{Hz}\), the period can be calculated as: \(T = 1/5.2\).
02

Calculate the wavelength

Using the wave speed formula \(v = f \lambda\), where \(v = 34 \mathrm{cm} / \mathrm{s}\) is the propagation speed, \(f = 5.2 \mathrm{Hz}\) is the frequency, and \(\lambda\) is the wavelength. Isolate for \(\lambda\) by dividing both sides of the equation by \(f\), yielding: \(\lambda = v / f\). Substituting the given values yields: \(\lambda = 34 \mathrm{cm} / \mathrm{s} / 5.2 \mathrm{Hz}\).
03

Perform necessary conversions

The above calculations will give results in seconds for the period and in cm for the wavelength. However, it might be more useful to have these answers in more widely usable units such as milliseconds for the period and meters for the wavelength. To convert from seconds to milliseconds, multiply by 1000. To convert from cm to meters, divide by 100.

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