Αποτελέσματα Αναζήτησης
The plus sign is used for waves moving in the negative x-direction. In summary, \(y(x, t)=A \sin (k x-\omega t+\phi)\) models a wave moving in the positive x-direction and \(y(x, t)=A \sin (k x+\omega t+\phi)\) models a wave moving in the negative x-direction. Equation \ref{16.4} is known as a simple harmonic wave function.
Define amplitude, frequency, period, wavelength, and velocity of a wave; Relate wave frequency, period, wavelength, and velocity; Solve problems involving wave properties
Where the waves meet in phase, constructive interference occurs so antinodes are formed, which are regions of maximum amplitude. Where the waves meet completely out of phase, destructive interference occurs and nodes are formed, which are regions of no displacement.
It has a maximum at z = 0 and a next maximum at k z = 2π. The separation between maxima is λ = 2π/k and is called the wavelength. After a time of t = 2π/ω the field reads E(r, t = 2π/ω) = E0 cos[k z − 2π] = E0 cos[k z], that is, the wave has prop-agated a distance of one wavelength in direction of z.
Find the amplitude, wavelength, period, and speed of the wave. Strategy All these characteristics of the wave can be found from the constants included in the equation or from simple combinations of these constants. Solution. The amplitude, wave number, and angular frequency can be read directly from the wave equation:
The amplitude of a wave is represented by the length of a “vector” on an Argand diagram. The phase of the wave is represented by the angle of the vector relative to the dsin d r 1 r 2 P D
Wave equations 1.1 Acoustic waves Acoustic waves are propagating pressure disturbances in a gas or liquid. With p(x;t) the pressure uctuation (a time-dependent scalar eld) and v(x;t) the particle velocity (a time-dependent vector eld), the acoustic wave equations read @v @t = 1 ˆ 0 rp; (1.1) @p @t = 0rv: (1.2) The two quantities ˆ 0 and
