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Write an equation for the wave as a function of position and time. A wave is modeled with the function y (x, t) = (0.25 m) cos (0.30 m −1 x − 0.90 s −1 t + π 3). 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.
Section 6.1 Exercises. 1. Sketch a graph of \(f\left(x\right)=-3\sin \left(x\right)\). 2. Sketch a graph of \(f\left(x\right)=4\sin \left(x\right)\). 3. Sketch a graph of \(f\left(x\right)=2\cos \left(x\right)\). 4. Sketch a graph of \(f\left(x\right)=-4\cos \left(x\right)\).
Problems for you to try: Complete the following practice problems. You MUST show ALL the work outlined in the steps in the example problems. A wave with a frequency of 14 Hz has a wavelength of 3 meters.
Sinusoidal waves render the mathematical analysis, in terms of differential equations, straightforward and, for linear systems, provide a complete basis set from which any solution can be formed as a superposition – even if the system shows dispersion.
Course: Precalculus > Unit 2. Lesson 7: Sinusoidal equations. Solving sinusoidal equations of the form sin (x)=d. Cosine equation algebraic solution set. Cosine equation solution set in an interval. Sine equation algebraic solution set. Solving cos (θ)=1 and cos (θ)=-1.
The sinusoidal wave is charaterised by. Wavenumber = k, Wavelength = 2 =k, Angular frequency ! = kc, Frequency f = !=2 , Period = 2 =!, Amplitude = C, and Phase = '. It is usually convenient to rewrite the sinusoidal wave as a complex exponential, cos(kx. !t + ') = Cei'eikx i!t + complex conjugate; 2. (2.2)
Some waves are periodic (particles undergo back and forth displacement as in a sound wave.) Some waves are sinusoidal (paricles undergo up and down displacement as in a wave on a string.) Electromagnetic. Examples -- light waves, radio waves, microwaves, X-rays, etc.
