Physics 106 Lesson #23 Dr. Andrew Tomasch 2405 Randall Lab WAVES

Energy Transfer How can energy get from Point A to Point B? –Objects can physically move from A to B. –Energy can be transferred thermally. Heat one end of a copper rod and after some time the other end becomes hot → Thermodynamics and Heat Transfer –A wave can propagate from A to B. This is happening as I speak to you (sound). As with thermal energy transfer, no particles are actually going from me to you. Unlike thermal transfer, the process is not chaotic and random. I speak and you hear my words (hopefully) clearly (a coherent process)

The Nature of Waves Two Defining Features: –A–A wave is a traveling disturbance –A–A wave transports energy one place to another Three Types of Waves: –T–Transverse: Electromagnetic Waves (radio, visible light, microwaves and X-Rays) –L–Longitudinal (sound waves) –S–Surface Waves: a combination of transverse and longitudinal waves (water waves)

Transverse and Longitudinal Waves Transverse –Definition: a disturbance perpendicular to the direction of travel –Example: transverse pulses on a slinky Longitudinal –Definition: a disturbance parallel to the direction of travel –Example: compression waves in a slinky Demo. Caution Quiz Ahead

Concept Test #1 With Michigan leading Ohio State 56-0 late in the third quarter, fans in Michigan stadium start to do “The Wave.” Is “The Wave” transverse or longitudinal? A.Transverse B.Longitudinal The displacement (people’s arms being raised over their heads) is perpendicular to the direction of motion (around the stadium) so the wave is transverse.

Periodic Waves  The pattern of the disturbance is repeated in time over and over again (periodically) by the source of the wave.  The red curve is a “snapshot” of the wave at t = 0  The blue curve is a “snapshot” later in time  A is a crest of the wave  B is a trough of the wave

Describing Periodic Waves  ≡ wavelength (distance between two successive corresponding points on the wave)  T ≡ period the time it takes for one wave cycle  A ≡ amplitude (largest displacement from equilibrium)  v ≡ the speed of the disturbance → the magnitude of the wave velocity Caution Quiz Ahead

Concept Test #2 WCBN-FM is the University of Michigan's student-run freeform radio station in Ann Arbor Michigan. It broadcasts at a frequency of 88.3 MHz. What is the wavelength of these radio waves? (The speed of light is 3.00×10 8 m/s and 1 MHz = 10 6 Hz ) A.3.4 m B.34 cm C.1 m D.15 cm v = λ f → λ = v/f = (3.00×10 8 m/s )/(88.3×10 6 Hz ) = 3.4 m

Waves on a String So far we have described the Kinematics –the what of wave motion What determines the properties of real waves? Dynamics: the why and how of wave motion. Set by the properties of the medium in which the wave propagates and Newton’s Second Law –The propagation speed will faster for a stiff medium with a large spring constant –The propagation speed will slower for a medium with a high inertia In general:

For a String –restoring force  tension in the string –inertia parameter  mass per unit length The speed of a wave on a string is greater for strings with a large tension and lower for thicker (heavier) strings compared to thinner strings placed under the same tension. This is a dynamics equation. It tells us how the speed of the wave is related to the physical parameters of the system. Waves on a String Caution Quiz Ahead

Concept Test #3 The speed of a transverse wave propagating on a string depends upon A. The amplitude of the wave B. The material properties of the string C. Both of the above D. Neither of the above Caution Quiz Ahead

Doubling the frequency of a wave source doubles the speed of the waves traveling along a string. True False Concept Test #4 The speed of the wave is determined by restoring force (tension) and inertia parameter (mass/unit length). With these two factors fixed changing f will result in a change in that keeps v constant.

Sound: A Pressure Wave Condensation ≡ region of increased pressure Rarefaction ≡ region of decreased pressure A pure tone is an harmonic (sine or cosine) sound wave with a single frequency

The energy of a sound wave propagates as an elastic disturbance through the air Individual air molecules do not travel with the wave A given molecule vibrates back and forth about a fixed location When we speak of sound, we mean frequencies within the range of human hearing: 20 H z < f < 20,000 H z Sound Waves Propagate in Air Ultrasonic: f > 20,000 Hz Example: bats echo locate objects with f > 60,000 Hz Infrasonic: f < 20 Hz Example: Whales

Interference Principle of Linear Superposition: –When adding one wave to another the resulting wave is the sum of the two original waves This leads to the phenomenon of interference: –Constructive interference: waves add to a larger amplitude –Destructive interference: waves add to smaller or zero amplitude. Constructive Destructive

Standing Waves Occur when a returning reflected wave interferes with the outgoing wave Special points: –nodes = places that do not vibrate at all –antinodes = maximum vibration at a fixed point Adjacent nodes are spaced a distance /2 apart /2

Transverse Standing Waves Occur when an outgoing wave interferes with (adds to) its reflection returning from the end of a string or pipe The standing wave motion is the sum of the individual motions of the two waves traveling in opposite directions at every point along the string (superposition) Unlike a traveling wave, a standing wave does not transfer energy from one place to another Nodes must occur at the ends of the string because these points are fixed and cannot move

Normal Modes of a String When both ends of a string with length L are held fixed, standing waves can occur only when L = (integer)  λ/2 /2=L 2( /2)=L 3( /2)=L

Longitudinal Standing Waves Standing sound waves (longitudinal standing waves) can be set up in a pipe or tube Wind instruments (trumpet, flute, clarinet, pipe organ, etc.) depend on longitudinal standing waves to produce sounds at specific frequencies (notes) Two kinds –Open Pipe: tube open at both ends –Stopped Pipe: tube open at only one end piccolo Demonstration

The length of the pipe is L Standing sound waves for the first two modes: “Stopped" Pipe (open on one end) "Open" pipe (open both ends) n=1 n=2 Stopped vs. Open Pipes