Whiteboard Work A child on a playground swing makes a complete to-and-fro swing every 2 seconds. What is the frequency of the swinging? What is the period of the swinging? For this lecture, have the following supplies &c: Demo equipment: table clamp, long coil spring, ropes of different weights, long slinky Websites: Dan Russel’s wave types animations, Northwestern’s Wave Superposition2 applet Sound files: beats Don’t forget the units!

Waves Part 1: Basics

Objectives Identify the parts of a wave. Relate wave speed, frequency, wavelength, and period. Trace the movement of the medium in a string wave, in a sound wave, and in a compression wave in a spring.

What’s the Point? How are waves described? Why do waves occur?

Week Outline Waves in One Dimension Combinations of Waves Features of Waves Types of Waves Combinations of Waves Interference Standing Waves

Waves and Vibrations Vibrations: Repeat in time no net displacement of disturbance no net displacement of medium Waves: Repeat in time and space wave travels

Features of a Wave crest trough Crest: high point Trough: low point Wavelength: crest-crest distance crest Period: crest-crest-timing Here we define names for wave features so that we can communicate easily. l trough

Features of a Wave Amplitude A: (crest height – trough height) / 2 Frequency f: repeats in a given time (= 1/T) Velocity u: speed of crest motion Here we define names for wave features so that we can communicate easily. u A

Relations between Features Period T = 1 / f ; Frequency f = 1 / T Velocity u = l / T = lf Wavelength l = uT = u / f Frequency f = u / l; Period T = l / u

Group Question Doubling the frequency of a wave while keeping its speed constant will cause its wavelength to increase. decrease. stay the same.

Group Question Doubling the speed of a wave while keeping its wavelength constant will cause its frequency to increase. decrease. stay the same.

Group Question Doubling the wavelength of a wave while keeping its frequency constant will cause its speed to increase. decrease. stay the same.

Group Whiteboard Work A wave generator produces 10 pulses each second. The pulses travel at 300 cm/s. What is the period of the waves? What is the wavelength of the waves?

Wave Pulse in a Rope Why does the pulse move? What determines its speed? What is happening inside the rope? Model: a chain of students holding hands, half-crouched. Tell them that the connections between them are like springs under tension and that their motions follow Newton’s Laws. Review: force proportional to spring displacement, acceleration follows force and mass, spring applies opposite force to segments on opposite ends.

Prediction Increasing the tension on a rope will make waves travel along the rope faster. slower. At the same speed (no effect). Demonstrate with coil spring or rope increasing tension. Rope is less ambiguous because its length density does not change appreciably with tension.

Prediction Increasing the length density (mass per meter) of a rope will make waves travel along the rope faster. slower. At the same speed (no effect). Demonstrate with two different ropes. They need to be fairly long.

Points to Ponder a c b d What are the velocity and acceleration of the string particles at the following positions? Why? middle (leading edge) crest middle (trailing edge) trough The particles of the string change their motion as the wave travels. What force accelerates them? Tension yields a net force where rope is curved. a is moving downward with momentarily zero acceleration b is momentarily motionless with downward acceleration c is moving upward with momentarily zero acceleration d is momentarily motionless with upward acceleration

Types of Waves Motion of the medium is perpendicular to the direction the wave travels: transverse wave (example: string wave) Motion of the medium is parallel to the direction the wave travels: longitudinal wave (examples: sound wave, slinky wave) Animation Crest and trough of a longitudinal wave: moving regions of highest and lowest pressure or density. Amplitude of a longitudinal wave: Half the total change in pressure or density

Question “The Wave” performed by sports fans is an example of a longitudinal wave. a transverse wave. an unnatural wave. Class activity: make a longitudinal audience wave

Combining Waves

Group Work Sketch the wave resulting from the addition of the two waves shown at one instant. 3 –3

Group Work Sketch the wave resulting from the addition of the two waves shown at one instant. 3 result –3

Interference Constructive: Sum of waves has increased amplitude Destructive: Sum of waves has decreased amplitude Two-wave simulation Run at: w1 = 0.2; k1 = 0.2; ampl = 15 integral multiples (half, third, quarter) of lambda: multiply W1, k1 by 2, 3, 4 add same-lambda wave with negative amplitude Beats: slightly vary w2 and k2 together from wave 1 values (0.22 and 0.22; 0.21 and 0.21, etc.) Standing waves (use w of about 0.2; try w = 0.2, k = 0.1)

Beats Waves of similar frequency combine to give alternating times of constructive and destructive interference Distinctive “waa-waa” sound with beat frequency equal to the difference in frequency of the component waves (Why?) (sound files)