lecture-ch16 - Contents 16 Waves-I 1 16.1 Types of Waves ....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Contents 16 Waves-I 1 16.1 Types of Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 1 16.1.1 Transverse Waves . . . . . . . . . . . . . . . . . . . . . 1 16.1.2 Longitudinal Waves . . . . . . . . . . . . . . . . . . . . 2 16.2 Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 3 16.3 Wavelength and Frequency . . . . . . . . . . . . . . . . . . . . 4 16.4 Speed for a Transverse Wave on a Stretched String . . . . . . 6 16.5 Energy and Power of a Traveling Wave Along a String . . . . 7 16.6 The Rate of Energy Transmission . . . . . . . . . . . . . . . . 8 16.7 The Principle of Superposition of Waves . . . . . . . . . . . . 9 16.8 Interference of Waves . . . . . . . . . . . . . . . . . . . . . . . 10 16.9 Standing Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 11 16.10Standing Waves and Resonances . . . . . . . . . . . . . . . . . 13 16.11Reflections at a Boundary . . . . . . . . . . . . . . . . . . . . 14 16 Waves-I Waves are one of the primary subjects in physics and play a crucial role in sound, light, and even quantum mechanics. In this chapter we will focus on waves traveling along a stretched string. 16.1 Types of Waves Mechanical waves: require a a material medium (water, air, rock, string) Electromagnetic waves: visible and invisible light (x-rays, ultraviolet light, visible light, microwaves, radar waves, radio and TV waves,). Travels in vacuum at speed c = 299 , 792 , 458 m/s . Matter waves: small particles (electrons, protons, etc) can behave like waves → quantum mechanics 16.1.1 Transverse Waves Displacement of every oscillating element, e.g., piece of string, is perpendic- ular to direction of wave travel. 1 16.1.2 Longitudinal Waves Displacement of every oscillating element, e.g., air molecules, is parallel to direction of wave travel. 2 In general, a one dimensional wave is a displacement y ( x, t ) , which is function of the space x and time t, moves without changing its form. i.e., as t → t + Δ t , the amplitude at space point x is displaced to the point x + Δ x = x + v Δ t y ( x, t ) = y ( x + Δ x, t + Δ t ) = y ( x + v Δ t, t + Δ t ) where v is called the wave speed. Let Δ t = − t , the above identity becomes y ( x, t ) = y ( x − vt, 0) = f ( x − vt ) (1) In other words, although the displacement y ( x, t ) is a function of two vari- ables x and t , it actually depends only the combination x − vt . 16.2 Wave Equation By (1), the partial derivatives ∂y ∂t and ∂y ∂x can be related to the ordinary derivative of f . To see this, let τ = x − vt . From the definition of partial derivative, we get ∂y ∂x = lim Δ x → y ( x + Δ x, t ) − y ( x, t ) Δ x = lim Δ x → f ( x + Δ x − vt ) − f ( x − vt ) Δ x = lim Δ...
View Full Document

This note was uploaded on 05/14/2011 for the course ECON 101 taught by Professor Asdaf during the Spring '11 term at Universidad de San Buenaventura Bogota.

Page1 / 14

lecture-ch16 - Contents 16 Waves-I 1 16.1 Types of Waves ....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online