Holt Physics Chapter 12 Waves

12-1 Periodic Motion A repeated motion that is back and forth over the same path.

12-2 Wave Properties

12-2 Period and Frequency Period and frequency measure time. or

12-3 Properties of Waves Wave: the motion of a disturbance. (SciLinks: HF2123, Wave motion)SciLinks Medium: the material through which a disturbance travels.

12-3 Types of Waves Mechanical Waves: A wave that propagates through a deformable, elastic medium. Pulse Wave: a single non-periodic disturbance. Periodic Wave: a wave whose source is some form of periodic motion.

12-3 Sine Waves Describe particles vibrating with simple harmonic motion.

12-3 Transverse Waves Vibrations are perpendicular to the wave motion.

12-3 Transverse Waves Crest: the highest point above the equilibrium position. Trough: the lowest point below the equilibrium position. Wavelength (λ): the distance between 2 adjacent similar points of the wave. Check out Holt Physics Interactive Tutor CD-ROM Module 12: Wave Frequency and Wavelength

12-3 Longitudinal (Compression) Waves A wave whose particles vibrate parallel to the direction of wave motion.

12-3 Graph of Longitudinal Wave

12-3 Wave Properties Period (T): amount of time required for one complete vibration or wave. (seconds) Frequency (f): number of waves per unit of time. (1/seconds = Hz) T = 1/f Speed of wave = frequency x wavelength v = λf = λ/T Waves transfer energy

Sample Problem 12D The piano string tuned to middle C vibrates with a frequency of 264 Hz. Assuming the speed of sound in air is 343 m s -1, find the wavelength of the sound waves produced by the string. v = λ f λ = v/f = 343 m s -1 / 264 Hz = 1.30 m

12-3 Review Graph (a) below describes the density versus time of a pressure wave traveling through an elastic medium. Graph (b) describes the density versus distance for the same wave. Use the graphs to find the period of oscillation, the frequency, the wavelength, and the speed of this wave.

14-2 Reflection The turning back of a wave at the boundary of a substance.

14-2 Law of Reflection Incident angle  : the angle between a ray that strikes a surface and the normal to that surface at the point of contact. Reflected angle  ’ : the angle between the normal to a surface and the direction in which a reflected ray moves. angle of incidence = angle of reflection

12-4 Reflection & Boundary Condition Free boundary: reflected pulse is erect. Fixed boundary: reflected pulse is inverted.

15-1 Refraction The bending of a wave disturbance as it passes at an angle from one medium into another. Occurs because wave speed changes.

15-1 Snell’s Law & Index of Refraction Snell’s law: The ratio of the speed of light in a vacuum to its speed in a medium. n = c/v Snell’s law for light:

Derivation of Snell’s Law using Huygen’s Principle The time it takes for A to reach y is the same time for X to travel to B. (AY = v 1 Δ t) and (XB = v 2 Δ t) NOW: (AY = XYsinθ 1 ) (XB = XYsinθ 2 ) Dividing the first by the second we get: (sinθ 1 /sinθ 2 = v 1 /v 2 ) Since v = c/n we can rearrange to get Snell’s Law: n 1 sinθ 1 =n 2 sinθ 2

As light travels between different substances (mediums) the speed and wavelength of light changes (low optical densities means faster, longer  high optical densities means slower, shorter ) FREQUENCY REMAINS CONSTANT!!!!

As the light travels from areas of low optical density to areas of high optical densities, the light ray tends to bend towards the normal Quiz time!

15-3 Total Internal Reflection Critical angle: the minimum incident angle for which the refracted angle is 90 .

Total internal reflection- complete reflection of light as it tries to pass from a high optical density to a low optical density; this occurs when the angle of incidence exceeds the critical angle. critical angle - minimum angle of incidence for which total internal reflection occurs sin  c = n r / n i  c - critical angle ( remember the angle is measured from the normal!!! ) n i must be greater than n r

Reflection vs. Transmission/Refraction

16-2 Diffraction The spreading of waves into a region behind an obstruction.

Diffraction Explained Huygen’s Principle

14-1 Huygen’s Principle A wave front can be divided into point sources. The line tangent to the wavelets from these sources marks the wave front’s new position. Ray approximation: a method of treating a propagating wave as a straight line perpendicular to the wave front.

12-4 Wave Interference When two wave interact as they pass through one another Superposition: Combination of two overlapping waves. Creates an interference pattern (SciLinks: HF2124, Electron microscope)SciLinks

12-4 Constructive Interference Interference in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave.

12-4 Destructive Interference Interference in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave.

12-4 Standing Waves A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. Node: a point in a standing wave that always undergoes complete destructive interference and therefore is stationary. Antinode: a point in a standing wave, halfway between two nodes, at which the largest amplitude occurs.

Standing Waves A standing wave is an interference pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. Node: a point that is always stationary. Antinode: a point that always has the largest amplitude.

12-4 Standing Waves

12-4 Fundamental Frequencies and Harmonics Only certain frequencies produce standing wave patterns. Fundamental = ½ λ 2 nd Harmonic = λ 3 rd Harmonic = 3/2 λ This means that : L = λ/2.

Resonance in Closed Pipes At the closed end, waves are reflected with a phase change of 180°, there is no displacement: a displacement node exists at the closed end. At the open end, the air is free to move; waves are reflected with no phase change so a displacement anti-node exists at the open end. Therefore, if waves take half a time period to travel twice the length of the pipe, resonance occurs and a loud sound is heard. For the fundamental frequency, f o, length of air column =  /4

Resonance in Open Pipes At an open end, waves are reflected without a change of phase. So, if waves travel twice the length of the pipe in one time period, they will return to the source in phase and constructive interference (resonance) will occur. At each end we have a large amplitude vibration: an anti- node of the stationary wave. The fundamental resonance is represented on the next diagram.

Sample Problem: An organ pipe closed at one end produces a fundamental note of frequency 440 Hz. What are the frequencies of the first two harmonics above the fundamental? What would be the frequency of the first two harmonics above the fundamental of a pipe of the same length but open at both ends? Taking the speed of sound to be 330 ms -1 estimate the length of the pipes.

12-4 Review 1.A stretched string fixed at both ends is 2.0 m long. A standing wave is produced on this string as shown in the following figure. How many nodes does this wave have? How many antinodes? What is the wavelength of this standing wave? 2.A 15.0 m long string is tied at one end (point B) and shaken repeatedly at the other end (point A) with a 2.00 Hz frequency. This generates waves that travel at 20.0 m s -1 in the string. A.How long does it take for each pulse to travel from A to B and return to A? B.What is the wavelength of these waves? C.Are the pulses inverted when reflected from B?