1. Physics 101: Lecture 32, Pg 1 Physics 101: Lecture 32 Waves and Sound l Today’s lecture will cover Textbook Sections 16.1 - 16.5 l Review: Simple Harmonic Motion (Chapter 10) Please check all of the entries in your grade book to make sure none of the grades are missing or messed up. Please contact your TA in case you have questions concerning your homework grades.

2. Physics 101: Lecture 32, Pg 2 Review: Simple Harmonic Motion l The position x of an object moving in simple harmonic motion as a function of time has the following form: x = A cos (  t) i.e. the object periodically moves back and forth between the amplitudes x=+A and x=–A. The time it takes for the object to make one full cycle is the period T=2  /  =1/f, where f is the frequency of the motion. Thus, the angular speed in terms of T and f reads  = 2  /T and  = 2  f

3. Physics 101: Lecture 32, Pg 3 What is a wave ? l Nature of waves: è A wave is a traveling disturbance that transports energy from place to place. è There are two basic types of waves: transverse and longitudinal. è Transverse: the disturbance travels perpendicular to the direction of travel of the wave. è Longitudinal: the disturbance occurs parallel to the line of travel of the wave. l Examples: è Longitudinal: Sound waves (e.g. air moves back & forth) è Transverse: Light waves (electromagnetic waves, i.e. electric and magnetic disturbances) The source of the wave, i.e. the disturbance, moves continuously in simple harmonic motion, generating an entire wave, where each part of the wave also performs a simple harmonic motion.

4. Physics 101: Lecture 32, Pg 4 Types of Waves l Longitudinal: The medium oscillates in the same direction as the wave is moving è Sound l Transverse: The medium oscillates perpendicular to the direction the wave is moving. è Water waves (also have a longitudinal component)

5. Physics 101: Lecture 32, Pg 5 Wave Properties Wavelength Wavelength: The distance between identical points on the wave. Amplitude A l Amplitude: The maximum displacement A of a point on the wave. A

6. Physics 101: Lecture 32, Pg 6 Wave Properties... l Period: The time T for a point on the wave to undergo one complete oscillation. Speed: The wave moves one wavelength in one period T so its speed is v =  / T.

7. Physics 101: Lecture 32, Pg 7 Wave Properties... l The speed of a wave is a constant that depends only on the medium, not on the amplitude, wavelength or period: and T are related ! = v T or = 2  v /  (since  T = 2  /   or  v / f (since T = 1/ f )   l Recall f = cycles/sec or revolutions/sec  2  f v = / T Is the speed of a wave particle the same as the speed of the wave ? No. Wave particle performs simple harmonic motion: v=A  sin  t.

8. Physics 101: Lecture 32, Pg 8 Concept Question Suppose a periodic wave moves through some medium. If the period of the wave is increased, what happens to the wavelength of the wave assuming the speed of the wave remains the same? 1. The wavelength increases 2. The wavelength remains the same 3. The wavelength decreases correct

9. Physics 101: Lecture 32, Pg 9 Concept Question The speed of sound in air is a bit over 300 m/s, and the speed of light in air is about 300,000,000 m/s. Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of the frequency of the light wave to that of the sound wave? 1. About 1,000,000. 2. About 1,000. 3. About 0.000001. correct f = v/ f L /f S = v L /v S = 1,000,000

10. Physics 101: Lecture 32, Pg 10 Transverse Waves on a String (e.g. Guitar) T=Tension : the greater the tension in the string the greater the pulling force the particles exert on each other and the faster the wave travels.  =mass/length of the string = m/L= linear density of the spring: the smaller the mass the greater the acceleration for the same pulling force and the faster the wave travels. Speed:

11. Physics 101: Lecture 32, Pg 11 Concept Question A rope of mass M and length L hangs from the ceiling with nothing attached to the bottom (see picture). Suppose you start a transverse wave at the bottom end of the rope by jiggling it a bit. As this wave travels up the rope its speed will: 1. Increase 2. Decrease 3. Stay the same the tension gets greater as you go up v correct

12. Physics 101: Lecture 32, Pg 12 Happy Thanksgiving !