Question

Assertion: In a harmonic progressive wave of a given frequency, all particles have the same phase but different amplitudes at a given instant of time. Reason: In a stationary wave, all particles between two nodes have the same amplitude at a given instant but have different phases.

Let us consider a familiar situation, a string fixed at either end or an air column in a pipe with either end closed in which reflection takes place at two or more boundaries. In a string, for example, a wave travelling in one direction will get reflected at one end, which in turn will travel and get reflected from the other end. This will go on until there is a steady wave pattern set up on the string. Such wave patterns are called standing waves or stationary waves. To see this mathematically, consider a wave travelling along the positive direction of x-axis and a reflected wave of the same amplitude and wavelength in the negative direction of x-axis. The Equations, with φ = 0, can be written as y1(x, t) = a sin (kx - ωt) y2(x, t) = a sin (kx + ωt) The resultant wave on the string is, according to the principle of superposition: y(x, t) = 2a sin kx cos ωt

Standing waves are produced due to superposition of two identical progressive waves travelling in

If equation of stationary wave is given by y = 15 sin 5x cos 8t. Calculate the wavelength.