UB, Phy101: Chapter 16, Pg 1 Physics 101: Lecture 27 Sound l Today’s lecture will cover Textbook Sections

UB, Phy101: Chapter 16, Pg 2 What is a wave ? l According to our text: è A wave is a traveling disturbance that transports energy l Examples: è Sound waves (air moves back & forth) è Stadium waves (people move up & down) è Water waves (water moves up & down) è Light waves (what moves ??) DEMO

UB, Phy101: Chapter 16, Pg 3 Types of Waves l Longitudinal: The medium oscillates in the same direction as the wave is moving è Sound è Slinky l Transverse: The medium oscillates perpendicular to the direction the wave is moving. è Water (more or less) è Slinky

UB, Phy101: Chapter 16, Pg 4 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

UB, Phy101: Chapter 16, Pg 5 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.

UB, Phy101: Chapter 16, Pg 6 Wave Properties... The speed of a wave is a constant that depends only on the medium, not on amplitude, wavelength or period (similar to SHM) 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

UB, Phy101: Chapter 16, Pg 7 Preflight 1 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

UB, Phy101: Chapter 16, Pg 8 Preflight 2 Preflight 2 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, About 1, About.000,001 correct f = v/ f L /f S = v L /v S = 1,000,000 f S = 100 Hz (~ really low G) f L = 100 MHz (FM radio)

UB, Phy101: Chapter 16, Pg 9 Preflight 3 & 4 Preflight 3 & 4 Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the slinky move through a distance of five meters in one second? 1. Yes 2. No no single coil on the slinky will move anywhere near 5 meters. Rather many coils will move many smaller distances in shorter times to create the wave that has a speed of 5 meters per sec. correct 5m

UB, Phy101: Chapter 16, Pg 10 l The wavelength of microwaves generated by a microwave oven is about 3 cm. At what frequency do these waves cause the water molecules in your burrito to vibrate ? (a) 1 GHz (b) 10 GHz (c) 100 GHz 1 GHz = 10 9 cycles/sec The speed of light is c = 3x10 8 m/s Another Question

UB, Phy101: Chapter 16, Pg 11 Recall that v = f. 1 GHz = 10 9 cycles/sec The speed of light is c = 3x10 8 m/s HH O Makes water molecules wiggle Another question, ans.

UB, Phy101: Chapter 16, Pg 12 Absorption coefficient of water as a function of frequency. f = 10 GHz Visible “water hole”

UB, Phy101: Chapter 16, Pg 13 Waves on a String

UB, Phy101: Chapter 16, Pg 14 Preflights 5 & 6 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 giggling (sic) 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

UB, Phy101: Chapter 16, Pg 15 Preflight A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the frequency of the sound wave inside and outside the balloon 1. f 1 < f 0 2. f 1 = f 0 3. f 1 > f 0 f1f1 f0f0 correct

UB, Phy101: Chapter 16, Pg 16 Preflight Preflight A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the speed of the sound wave inside and outside the balloon 1. v 1 < v 0 2. v 1 = v 0 3. v 1 > v 0 V 1 =965m/s V 0 =343m/s correct

UB, Phy101: Chapter 16, Pg 17 Preflight Preflight A sound wave having frequency f 0, speed v 0 and wavelength 0, is traveling through air when in encounters a large helium-filled balloon. Inside the balloon the frequency of the wave is f 1, its speed is v 1, and its wavelength is 1 Compare the wavelength of the sound wave inside and outside the balloon 1. 1 < = > correct = v / f

UB, Phy101: Chapter 16, Pg 18 Doppler Effect DEMODEMO

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UB, Phy101: Chapter 16, Pg 21

UB, Phy101: Chapter 16, Pg 22 Preflight A: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on. B: You and the police car have both pulled over to the side of the road, but the siren is still turned on. In which case does the frequency of the siren seem higher to you? 1. Case A 2. Case B 3. same vsvs f vovo f’ v correct Pg 479 NOT ON EXAM

UB, Phy101: Chapter 16, Pg 23 Constructive interference Destructive interference Interference and Superposition

UB, Phy101: Chapter 16, Pg 24 Superposition & Interference l Consider two harmonic waves A and B meeting at x=0.  Same amplitudes, but  2 = 1.15 x  1. l The displacement versus time for each is shown below: What does C(t) = A(t) + B(t) look like?? A(  1 t) B(  2 t)

UB, Phy101: Chapter 16, Pg 25 Superposition & Interference l Consider two harmonic waves A and B meeting at x = 0.  Same amplitudes, but  2 = 1.15 x  1. l The displacement versus time for each is shown below: A(  1 t) C(t) = A(t) + B(t) CONSTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE B(  2 t)

UB, Phy101: Chapter 16, Pg 26

UB, Phy101: Chapter 16, Pg 27 Beats l Can we predict this pattern mathematically? è Of course! l Just add two cosines and remember the identity: whereand cos(  L t)

UB, Phy101: Chapter 16, Pg 28 Standing Waves: Fixed “nodes” HW: Airport

UB, Phy101: Chapter 16, Pg 29 Standing Waves: f 1 = fundamental frequency (lowest possible) L  / 2 f 2 = first overtone L  f = v /  tells us f if we know v and