(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 node and antinode of a stationary wave
(iii) List the factors on which the frequency of vibration in a stretched string depends
(c) The equation, y = 5 sin (3x – 4t), where y is in millimeters, x is in meres and t is in seconds represents a wave motion . Determine the;
(i) frequency
(ii) period
(iii) speed of the wave
Explanation
a) (i) A wave motion is a disturbance which travels through a medium and transfers energy from one point to another without causing any permanent displacement of the medium itself.
(ii) A stationary wave is a wave got when two progressive waves of equal amplitude and frequency or wavelength travelling in opposite direction are superimposed. In stationary wave nodes are pendulum of permanently at rest while antinodes are at maximum amplitude
Stationary wave along a string
(b)(i) Physical properties of wave are: diffraction, refraction, reflection and.interference.
(ii) Amplitude is the maximum displacement of a oscillating object from its equilibrium position. A node is a point on a stationary wave at zero amplitude while an antinode is a point at maximum amplitude.
(iii) Frequency of vibration on a stretch string depends on;
- Tension on the string
- Length of stretch string
- Mass per unit length and density of the string
(c) y = 5 sin (3x - 4t); y = A sin (\(\frac{2 \pi x}{\pi} \times 2 \pi ft\))
\(\frac{2 \pi x}{\pi}\) = 3x
\(\pi = \frac{2 \pi}{3}\)m = 2\(\pi ft\) = 4t
f = \(\frac{2}{\pi }\)
(i) = \(\frac{2}{\pi}\) = 0.64Hz
(ii) T = \(\frac{1}{f}\) = \(\frac{1}{0.64}\) = 1.56(s)
(iii) V = f\(\pi\) = 0.64 x \(\frac{2 \pi}{3} = 1.34\)m/s