Topic 4.4 Wave Characteristics (2 hours) You must live in the present, launch yourself on every wave, find your eternity in each moment. Henry David Thoreau 1
What s a wave? A wave is a disturbance that transfers energy from one place to another. The direction of energy transfer is the direction of propagation of the wave. There is no net motion of the medium through which the wave travels. 2
Transverse and Longitudinal Waves A transverse wave is a wave in which the disturbance is at right angles to the direction of propagation of the wave. NOTE: Transverse waves cannot be propagated in gases. Ex. A wave set up on a guitar string. Ex. Electromagnetic waves are transverse waves. A longitudinal wave in a wave in which the disturbance is along the direction of propagation of the wave. Ex. Sound waves travel longitudinally. 3
Transverse and Longitudinal Waves Crest Crest Crest Trough Trough Compression Rarefaction 4
Parts of Waves Crests The highest points on a transverse wave. Troughs The lowest points on a transverse wave. Compression The region of a longitudinal wave in which the distance separating the vibrating particles is less than their equilibrium distance. Rarefaction The region of a longitudinal wave in which the vibrating particles are farther apart then their equilibrium distance. 5
Wave Pulses If you tie one end of a rope to a wall and move the other end sharply and then back down to its starting position you will set up a wave pulse in the rope. Direction of Motion Direction of Disturbance 6
Pulse Speed The wave pulse travels down the string with a certain speed. In the case of a wave pulse on a rope the speed is determined not by the way in which the pulse was created (big or small, wide or narrow) nor by how fast or slow you moved your hand. 7
Pulse Speed It depends only on the tension (T) in the rope and its mass per unit length (µ = m/l) The speed of a pulse (v) on a string is given by NOTE: The speed is determined by the properties of the medium and not by how the wave was created. 8
Travelling Waves We can create a travelling wave by producing one pulse after another. A harmonic wave will look like a sine wave. While a sequence of square pulses will produce a travelling square wave. 9
Describing Waves Amplitude (A) The maximum displacement from the equilibrium position. (measured in m) NOTE: The intensity of a wave is proportional to the square of its amplitude. Amplitude (A) Amplitude (A) Amplitude (A) 10
Describing Waves Wavelength (λ) the distance between any two successive points in phase. (measured in m) Wavelength (λ) Wavelength (λ) Wavelength (λ) 11
Describing Waves Period (T) the amount of time for one complete cycle. (measured in s) Period (Τ) Period (Τ) Period (Τ) 12
Describing Waves Frequency (f) the number of cycles per unit time. (measured in Hz or s 1 ) Speed (v) the distance per unit time a wave travels in its direction of propagation. (measured in m/s) 13
Phase Phase is used to describe the position and direction of motion of a particle on a wave. Two particles are in phase if they have the same displacement and are moving in the same direction. Two particles have opposite phase if they have opposite displacements and are moving in opposite directions. 14
Frequency and Period The period is the amount of time for one complete cycle. T = t/n units: T = s/cycles = s The frequency is the number of cycles per unit time. f = N/ t units: f = cycles/s = s 1 = Hz The frequency is therefore the reciprocal of the period. f = 1/T or T = 1/f 15
The Wave Equation 16
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Homework: Tsokos Pages 225 227 Questions 2, 3, 5, 6, 7, 8, 15 Questions 11, 16, 17, 18, 20 18
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