(a) Explain; (i) wave motion (ii) stationary wave (b)(i) List four physical properties of a wave (ii) Define amplitude and use it to distinguish between the...

Answer Details

(a)(i) Wave motion: a disturbance that travels through a medium (or space) transferring energy from one point to another without any bulk transfer of the particles of the medium; the particles merely vibrate about their fixed mean positions.

(ii) Stationary (standing) wave: a wave formed when two progressive waves of the same frequency and amplitude travelling in opposite directions superpose; it has fixed points of zero amplitude (nodes) and points of maximum amplitude (antinodes), and the wave profile does not advance.

(b)(i) Four physical properties of a wave: amplitude, wavelength, frequency (or period), and speed (velocity).

(ii) Amplitude is the maximum displacement of a particle from its equilibrium (mean) position. In a stationary wave, a node is a point of zero amplitude (the particles do not move), while an antinode is a point of maximum amplitude.

(iii) The frequency of vibration of a stretched string depends on its length, the tension in the string, and its mass per unit length (linear density).

(c) Comparing \(y = 5\sin(3x - 4t)\) with \(y = A\sin(kx - \omega t)\): \(A = 5\ \text{mm}\), \(k = 3\ \text{m}^{-1}\), \(\omega = 4\ \text{rad s}^{-1}\).

(i) Frequency:

\[ f = \frac{\omega}{2\pi} = \frac{4}{2\pi} = 0.637\ \text{Hz} \]

(ii) Period:

\[ T = \frac{1}{f} = \frac{2\pi}{\omega} = \frac{2\pi}{4} = 1.57\ \text{s} \]

(iii) Speed:

\[ v = \frac{\omega}{k} = \frac{4}{3} = 1.33\ \text{ms}^{-1} \]

(Equivalently \(v = f\lambda\), with \(\lambda = \tfrac{2\pi}{k} = 2.09\ \text{m}\).)