Αποτελέσματα Αναζήτησης
Give one example of a transverse wave and one example of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each. A sinusoidal transverse wave has a wavelength of 2.80 m.
Write down the solution of the wave equation u tt = u xx with ICs u (x; 0) = f (x) and u t (x; 0) = 0 using D'Alembert's formula. Illustrate the nature of the solution by sketching the ux -pro les y = u (x; t) of the string displacement for t = 0 ; 1=2; 1; 3=2. Solution: D'Alembert's formula is 1 Z x+t
K1. Vocabulary: amplitude, wavelength, wave number, phase, phase constant, wave function, wave speed, wave equation, harmonic function, sinusoidal wave, traveling wave, boundary conditions, ̄eld.
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.
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.
A student makes the following statements about waves. I Waves transfer energy. II A wave with a short wavelength diffracts more than a wave with a long wavelength.
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.
