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Define amplitude, frequency, period, wavelength, and velocity of a wave; Relate wave frequency, period, wavelength, and velocity; Solve problems involving wave properties
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.
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.
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.
1. 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 \\ &\left(A=0.2 \: \mathrm{m} ; k=6.28 \: \mathrm{m}^{-1} ; \omega=1.57 \: \mathrm{s}^{-1}\right) \nonumber
We will use the formulas \(k=2\pi/\lambda\) and \(\omega=2\pi f\) to rewrite this equation in the form \(D=(a(t\pm x/v))\). The frequency, \(f\), of the wave will be the same in both ropes. The velocity of the wave, and therefore its wavelength, depends on the mass density of the rope.
The amplitude of a wave is the maximum displacement of the particle of the medium from its equilibrium position. Check this page to know the formula for Amplitude with Solved Example.