The Science of Waves
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The document provides an introductory lesson on waves, explaining them as disturbances that carry energy and momentum rather than the actual movement of matter. It categorizes waves into mechanical, non-mechanical, and matter waves, detailing their characteristics and behavior, including types like transverse and longitudinal waves. The document also describes wave properties such as amplitude, wavelength, and examples while discussing phenomena like standing waves and shock waves.
The Science of Waves
- 1. Welcome friends! Today, we’ll be learning about
- 2. WAVES? You mean the movement of flags? No, No, a wave is not just the movement of a flag or any other thing. It’s a sort of disturbance which carries energy and momentum. Sir, I still don’t get it. I’m bad at physics. Can you please explain it in detail. Sure, no problem, let’s begin students!
- 3. Imagine that you’re near a pond/lake and you’re throwing pebbles/stones into it. What do you observe? After the stone is dropped, you can see concentric circles moving around the point where the stone was thrown. These concentric circles are called ripples, and they would look something like this…
- 4. Thus, as you can see, the surface of the water is disturbed by the stone throw. If you continue to throw stones, you can observe that the ripples move outward along a circle. You may feel that the water is moving outward from the disturbed surface, but actually the water doesn’t move at all. In fact, it just moves Up & Down. So we can say that a moving disturbance is created, rather than any real propagation of the water.
- 5. Thus, patterns such as ripples on the surface of water, which move without the actual transfer or flow of matter as a whole, are called waves. Wow! So much to know about waves! I want to know more! Sure! and now, let’s learn about what they do, how they look, and how many types of waves are there…. Waves transport energy & the pattern of disturbance has information that propagate from one point to another Well? What do you think students?
- 6. But Sir, how does a wave look like? Let us do a small experiment to ‘see’ how a wave looks like: Consider a collection of springs connected to one another as shown: If the spring k3 is pulled and released suddenly, the disturbance travels to the other end. It is observed that each string is pulled;k3 pulls k2 which in turn pulls k1, thereby propagating the disturbance.
- 7. Is there more than just one type of wave? Waves are of three types: 1. Mechanical Waves – Waves which require material medium to propagate Examples : Sound waves, seismic waves, ripples on surface of water 2. Non-Mechanical Waves (Electromagnetic waves) - Waves which don’t require a material medium to propagate. Examples: Light, Radio Waves, Ultra-violet waves 3. Matter Waves – Waves associated with the constituents of matter. For now, we shall learn in detail about Mechanical Waves…
- 8. Mechanical Waves Waves which require a material medium to propagate. Sound waves Ripples on the surface of water Seismic waves
- 9. Transverse Waves Transverse Waves: Waves whose vibrations of the particles are perpendicular to the direction of propagation of the wave, are called Transverse waves. Examples: Light waves, radio waves etc.
- 10. Longitudinal Waves Longitudinal Waves: Waves whose vibrations of the particles are parallel to or along the direction of propagation of the wave, are called Longitudinal waves. Examples: Sound waves, Seismic waves etc
- 11. How do these waves behave? Mechanical waves are related to the elastic property of the medium. In Transverse waves, the constituents of the medium oscillate perpendicular to the wave motion causing change in shape, hence they’re subject to shearing stress. Fluids have no shape, and thus they only yield to shearing stress. This is the reason why transverse waves are not possible in solids & strings, but not in fluids. Longitudinal waves possess both bulk & sheer elastic moduli and can travel longitudinal as well as transverse waves.
- 12. Basic parts of a wave The maximum displacement of a wave from it’s equilibrium position (initial position) is called the Amplitude of the wave. On a plane, the maximum displacement along the positive y-axis is called the Crest, whereas the maximum displacement along the negative y-axis is called the Trough. The distance between two consecutive Troughs, or two consecutive Crests is called Wavelength.
- 13. Dimensional Waves: One Dimensional Wave Waves which travel along a straight line are called One-dimensional Waves. The most basic One Dimensional Wave is the Sine Wave or Sinusoidal Wave. Another example of One Dimensional Waves are the waves produced on a Stretched String. Sine Wave Wave on stretched string
- 14. Dimensional Waves: Two Dimensional Wave Waves which travel along a plane are called Two-dimensional Waves. On the plane, these waves travel along both the x-axis & the y-axis. These waves look like this… A two-dimensional wave on a disk in normal mode Dispersion of light is a two-dimensional wave.
- 15. Dimensional Waves: Three Dimensional Wave Waves which travel in space, in all three dimensions are called Three-dimensional Waves. Sound is a good example for a three-dimensional wave. Electromagnetic Wave is a special wave in which two waves (electric & magnetic waves) travel perpendicular to each other and propagate forward simultaneously, together travelling in three- dimensions. Three-dimensional propagation of sound waves Three-dimensional propagation EM Waves
- 16. Dimensional Waves: Stationary Waves A standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or; it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions; In another case, for waves of equal amplitude traveling in opposing directions, there is, on an average, no net propagation of energy.
- 17. Dimensional Waves: Shock Waves A shock wave (also called shock front or simply "shock") is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a filed such as the electromagnetic field. A shock wave travels through most media at a higher speed than an ordinary wave. A shock wave produced by a supersonic body (jet)Shadowgraph of a shock wave produced by a supersonic bullet
- 18. Matter Waves: de Broglie’s Waves The Schrödinger equation describes the wave-like behaviour of particles in quantum mechanics. Using his theories, Louis de Broglie postulated that all particles with momentum have a wavelength 𝝀 = 𝒉 𝒑 where h is Planck's constant, and p is the magnitude of the momentum of the particle, and 𝛌 is the wavelength of the wave, now-a-days called as the de Broglie’s wavelength. de Broglie’s wave propagation
- 19. Sound Waves As waves passes through air, it compresses and expands a small region of air, called Compressions & Rarefactions, respectively. This causes a change in density ∆𝛒 and induces a change in pressure ∆𝐩 in that region. These changes disturb the air molecules, thereby propagating the disturbance and thus producing sound.
- 20. Wow! I learnt so much today…All about waves! I am so much interested in waves that I want to learn more. Hmm But you have learnt enough for today. We’ll resume next time Hope you enjoyed my teaching! Have a nice day!