NJC 2022 Waves Notes

National Junior College 2022 2022 | Science | JH4 Bridging Module WAVES Overview Waves are inherent in our everyday lives. Much of our understanding of wave phenomena has been accumulated over the centuries through the study of light (optics) and sound (acoustics). The nature of oscillations in light was only understood when James Clerk Maxwell, in his unification of electricity, magnetism and electromagnetic waves, stated that all electromagnetic fields spread in the form of waves. Using a mathematical model (Maxwell’s equations), he calculated the speed of electromagnetic waves and found it to be close to the speed of light, leading him to make a bold but correct inference that light consists of propagating electromagnetic disturbances. This gave the very nature of electromagnetic waves, and hence its name. In this bridging course, we examine the nature of waves in terms of the coordinated movement of particles. The discussion moves on to wave propagation and its uses by studying the properties of light, electromagnetic waves and sound, as well as their applications in wireless communication, home appliances, medicine and industry. There are 4 topics in this course: 1. General Wave Properties 2. Light 3. Electromagnetic Spectrum 4. Sound

JH4 Bridging Module (2022) 2 Topic 1: General Wave Properties Content • Describing wave motion • Wave terms • Longitudinal and transverse waves Learning Outcomes Students should be able to: (a) describe what is meant by wave motion as illustrated by vibrations in ropes and springs (b) compare transverse and longitudinal waves and give suitable examples of each (c) show understanding that waves transfer energy without transferring matter (d) define speed, frequency, wavelength, period and amplitude (e) recall and apply the relationship velocity = frequency × wavelength to new situations or to solve related problems (f) recall that a ripple tank can be used to demonstrate water waves (g) state what is meant by the term wavefront 1.1 Types of wave motion (a) describe what is meant by wave motion as illustrated by vibrations in ropes and springs (b) compare transverse and longitudinal waves and give suitable examples of each (c) show understanding that waves transfer energy without transferring matter Several kinds of wave motion occur in physics. Mechanical waves are produced by a disturbance, such as a vibrating object, in a material medium and are transmitted by the particles of the medium vibrating about a fixed position. Such waves can be seen or felt and include waves on a rope or spring, water waves and sound waves in air or in other materials. A progressive wave or travelling wave is a disturbance which carries energy from one place to another without transferring matter. There are two types, transverse and longitudinal waves. Transverse waves In a transverse wave, the direction of the disturbance is at right angles to the direction of propagation of the wave, that is the direction in which the wave travels. A transverse wave can be sent along a rope (or a spring) by fixing one end and moving the other rapidly up and down (Fig. 1.1). The disturbance generated by the hand is passed on from one part of the rope to the next which performs the same motion but slightly later. The humps and hollows of the wave travel along the rope as each part of the rope vibrates transversely about its undisturbed position.

JH4 Bridging Module (2022) 3 Fig. 1.1 The motion of the wave down the rope carries the energy provided by the hand towards the anchor point of the rope. The rope acts as the medium for the transverse wave to propagate while it remains intact, so there is no transfer of matter. Longitudinal waves In a progressive longitudinal wave the particles of the transmitting medium vibrate back and forth along the same line as (parallel to) that in which the wave is travelling and not at right angles to it as in a transverse wave. A longitudinal wave can be sent along a spring (or slinky), stretched out on the bench and fixed at one end, if the free end is repeatedly pushed and pulled sharply, as shown in Fig. 1.2. Fig. 1.2 Compressions C (where the coils are closer together) and rarefactions R (where the coils are further apart) travel along the spring. The motion of the compressions and rarefactions wave down the spring carries the energy from the right hand towards the fixed end. The spring acts as the medium for the longitudinal wave to propagate while it remains intact, so there is no transfer of matter.

JH4 Bridging Module (2022) 4 1.2 Describing Waves (d) define wavelength, amplitude, period and frequency (e) recall and apply the relationship speed of wave = frequency × wavelength to new situations or to solve related problems Displacement–distance graph Terms used to describe waves can be explained with the aid of a displacement–distance graph (Fig. 1.3). It shows, at a certain instant of time, the distance moved (sideways from their undisturbed positions) by the parts of the medium vibrating at different distances from the cause of the wave. Fig. 1.3 Wavelength The wavelength of a wave, represented by the Greek letter λ (‘lambda’), is the distance between successive crests (peaks). Amplitude The amplitude a is the height of a crest or the depth of a trough measured from the undisturbed (or equilibrium) position of what is carrying the wave. Deducing the direction of motion of points on a wave The short arrows at A, B, C, D on Fig.1.3 show the directions of vibration of the parts of the rope at these points. How do we deduce the direction of motion of these points on the wave? Fig. 1.4 shows a progressive transverse wave moving to the right. Fig. 1.4 (1) maximum displacement from the equilibrium(2) point is momentarily at rest at the instant(3) point will accelerate and move upwards (1) zero displacement from the equilibrium at the instant(2) point moving upwards (1) zero displacement from the equilibrium at the instant(2)point moving downwards wave at a later instant

JH4 Bridging Module (2022) 5 The points on the rope A, B and C on the rope at the instant shown (solid line) must take up new positions to form the new wave at a later instant (dotted line). This method allows use to deduce the direction of motion of any points on the wave at a particular instant. Phase Phase State of the vibration or oscillation of a point on a wave. The short arrows at A, B, C, D on Fig.1.3 show the directions of vibration of the parts of the rope at these points. • A and C have the same speed in the same direction and are in phase. • B and D are also in phase with each other but they are out of phase with those at A and C because their directions of vibration are opposite. In general, Two points on a wave that are integer multiples of the wavelength (λ, 2 λ, 3λ, …) apart are in phase. Displacement–time graph If we track the displacement of a point in the medium, for example point B or D in Fig. 1.3, we obtain a displacement–time graph (Fig. 1.5). Fig. 1.5 Period Time taken T for one complete oscillation of a point of the wave. amplitudea displacement time period T period T

JH4 Bridging Module (2022) 6 Frequency Frequency The frequency f is the number of complete waves generated per unit time. The frequency of a wave is also the number of crests passing a chosen point per unit time. Fig. 1.6 A progressive wave propagates in a medium. Fig. 1.6 shows waves generated by a mechanical vibrator on a string at two certain instants of time, time = 0 and time = 1 second. We noticed that • when the vibrator moves the end of a rope moved up and down three times in a second and three waves crests are produced in this time, • three wave crests pass point P. We say that the frequency of the wave is three vibrations per second or 3 hertz (3 Hz; the hertz is the unit of frequency), whic