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Chapter 14: Problem 22

An ocean wave has period 4.1 s and wavelength 10.8 \(\mathrm{m}\). Find its (a) wave number and (b) angular frequency.

Short Answer

Expert verified
The wave number is approximately \(0.093\) \(\mathrm{m^{-1}}\) and the angular frequency is approximately \(1.53\) \(\mathrm{s^{-1}}\).

Step by step solution

01

Calculate the Wave Number

The wave number \(\mathrm{k}\) is in fact the spatial frequency of the wave, which is the quantity of wavelengths per unit distance. The wave number is defined as the inverse of the wavelength \(\mathrm{\lambda}\). Hence, \(\mathrm{k} = \frac{1}{\lambda}\). Based on the given exercise, we substitute \(\lambda = 10.8 \, \mathrm{m}\) into the formula and carry out the calculation to find \(\mathrm{k}\).
02

Calculate the Angular Frequency

The angular frequency \(\mathrm{\omega}\) is the rate of change of the function argument in units of radian per second. The angular frequency is computed by the formula \(\mathrm{\omega} = \frac{2\pi}{T}\), where \(T\) is the period. Given in the exercise \(T = 4.1 \, \mathrm{s}\), we substitute this into the formula and perform the calculation to yield the angular frequency.

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