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Find the (a) amplitude, (b) wave number, (c) angular frequency, (d) wave speed, (e) initial phase shift, (f) wavelength, and (g) period of the wave. A surface ocean wave has an amplitude of 0.60 m and the distance from trough to trough is 8.00 m.
- 16.3: Mathematics
The amplitude, wave number, and angular frequency can be...
- 16.3: Mathematics
Define amplitude, frequency, period, wavelength, and velocity of a wave; Relate wave frequency, period, wavelength, and velocity; Solve problems involving wave properties
Amplitude is something that relates to the maximum displacement of the waves. Furthermore, in this topic, you will learn about the amplitude, amplitude formula, formula’s derivation, and solved example.
In the previous section, we described periodic waves by their characteristics of wavelength, period, amplitude, and wave speed of the wave. Waves can also be described by the motion of the particles of the medium through which the waves move.
The amplitude, wave number, and angular frequency can be read directly from the wave equation: \begin{align*} y(x, t)=& A \sin (k x-w t)=0.2 \: \mathrm{m} \sin \left(6.28 \: \mathrm{m}^{-1} x-1.57 \: \mathrm{s}^{-1} t\right) \nonumber \\
This collection of problem sets and problems target student ability to use basic mathematical ideas such as frequency, period, wavelength, amplitude, and wave speed to analyze situations and solve problems associated with vibrations and waves.
Analyze standing wave situations to relate the frequency, wavelength, speed harmonic pattern (or number), and the number of vibrations in a given amount of time. Includes 7 problems.
