1. Chapter 16: Sound

2. Problem 44
44. (II) A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe?

3. Problem 46
46. (II) A uniform narrow tube 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?

4. 16-4 Sources of Sound: Vibrating Strings and Air Columns
Wind instruments create sound through standing waves in a column of air.
The lip of the player will set up the vibrations of the air column.
In a uniform narrow tube such as a flute or an organ pipe, the shape of the waves are simple.
Figure Wind instruments: flute (left) and clarinet.

5. 16-5 Quality of Sound, and Noise; Superposition
So why does a trumpet sound different from a flute? The answer lies in overtones —which ones are present, and how strong they are, makes a big difference. The sound wave is the superposition of the fundamental and all the harmonics.
Figure The amplitudes of the fundamental and first two overtones are added at each point to get the “sum,” or composite waveform.

6. 16-6 Interference of Sound Waves; Beats
Sound waves interfere in the same way that other waves do in space.
Figure Sound waves from two loudspeakers interfere.
Figure Sound waves of a single frequency from loudspeakers A and B (see Fig. 16–15) constructively interfere at C and destructively interfere at D. [Shown here are graphical representations, not the actual longitudinal sound waves.]
The difference BE has to be n(1/2)λ of the sound for
destructive interference
to occur

7. 16-6 Interference of Sound Waves; Beats
Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow “envelope” around two waves that are relatively close in frequency.
Figure Beats occur as a result of the superposition of two sound waves of slightly different frequency.

8. 16-6 Interference of Sound Waves; Beats
If we consider two waves of the same amplitude and phase, with different frequencies, we can find the beat frequency when we add them:
This represents a wave vibrating at the average frequency, with an “envelope” at the difference of the frequencies.
The beat frequency is the difference in the two frequencies.

9. 16-6 Interference of Sound Waves; Beats
Example 16-12: Loudspeakers’ interference.
Two loudspeakers are 1.00 m apart. A person stands 4.00 m from one speaker. How far must this person be from the second speaker to detect destructive interference when the speakers emit an 1150-Hz sound? Assume the temperature is 20°C.
Solution: The wavelength is 0.30 m. For destructive interference, the person must be half a wavelength closer or farther away, 3.85 m or 4.15 m.

10. 16-6 Interference of Sound Waves; Beats
Example 16-13: Beats.
A tuning fork produces a steady 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible frequencies produced by the guitar string?
Solution: The beat frequency is 4 Hz, so the string is either 396 or 404 Hz.

11. Problem 54
54. (I) What is the beat frequency if middle C (262 Hz) and (277 Hz) are played together? What if each is played two octaves lower (each frequency reduced by a factor of 4)?

12. 16-7 Doppler Effect

13. 16-7 Doppler Effect
The Doppler effect occurs when a source of sound is moving with respect to an observer.
A source moving toward an observer appears to have a higher frequency and shorter wavelength; a source moving away from an observer appears to have a lower frequency and longer wavelength.
Figure (a) Both observers on the sidewalk hear the same frequency from a fire truck at rest. (b) Doppler effect: observer toward whom the fire truck moves hears a higher-frequency sound, and observer behind the fire truck hears a lower-frequency sound.

14. 16-7 Doppler Effect The change in the frequency is given by:
If the source is moving toward the observer
If the source is moving away from the observer:

15. 16-7 Doppler Effect
If the observer is moving with respect to the source, things are a bit different. The wavelength remains the same, but the wave speed is different for the observer.
Figure Observer moving with speed vobs toward a stationary source detects wave crests passing at speed v’ = vsnd + vobs, where vsnd is the speed of the sound waves in air.

16. 16-7 Doppler Effect
We find, for an observer moving toward a stationary source:
And if the observer is moving away:

17. Chapter 17 Heat and the First Law of Thermodynamics
Chapter opener. When it is cold, warm clothes act as insulators to reduce heat loss from the body to the environment by conduction and convection. Heat radiation from a campfire can warm you and your clothes. The fire can also transfer energy directly by heat convection and conduction to what you are cooking. Heat, like work, represents a transfer of energy. Heat is defined as a transfer of energy due to a difference of temperature. Work is a transfer of energy by mechanical means, not due to a temperature difference. The first law of thermodynamics links the two in a general statement of energy conservation: the heat Q added to a system minus the net work W done by the system equals the change in internal energy ΔEint of the system: ΔEint = Q – W. Internal energy Eint is the sum total of all the energy of the molecules of the system.

18. 17-1 Temperature: Atomic Theory of Matter
Atomic and molecular masses are measured in unified atomic mass units (u). This unit is defined so that the carbon-12 atom has a mass of exactly u. Expressed in kilograms:
1 u = x kg.
Brownian motion is the jittery motion of tiny pollen grains in water; these are the result of collisions with individual water molecules.
Figure Path of a tiny particle (pollen grain, for example) suspended in water. The straight lines connect observed positions of the particle at equal time intervals.

19. 17-1 Atomic Theory of Matter
On a microscopic scale, the arrangements of molecules in solids (a), liquids (b), and gases (c) are quite different.
(a)
(b)
Figure Atomic arrangements in (a) a crystalline solid, (b) a liquid, and (c) a gas.
(c)

20. 17-2 Temperature and Thermometers
Temperature is a measure of how hot or cold something is.
Most materials expand when heated: An Iron beam is longer when hot than when cold
Concrete roads expand and
contract slightly with temperature
Figure Expansion joint on a bridge.
Expansion joint on a bridge

21. 17-2 Temperature and Thermometers
Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature.
Early thermometers:
Built by Accademia del
Cimento ( ) in
Florence, Italy
Figure Thermometers built by the Accademia del Cimento (1657–1667) in Florence, Italy, are among the earliest known. These sensitive and exquisite instruments contained alcohol, sometimes colored, like many thermometers today.

22. 17-2 Temperature and Thermometers
Figure Celsius and Fahrenheit scales compared.

23. 17-2 Temperature and Thermometers
Example 17-2: Taking your temperature.
Normal body temperature is 98.6°F. What is this on the Celsius scale?
Solution: Conversion gives 37.0 °C.

24. Problem 3
3. (I) (a) “Room temperature” is often taken to be 68°F. What is this on the Celsius scale? (b) The temperature of the filament in a lightbulb is about 1900°C. What is this on the Fahrenheit scale?

25. 17-3 Thermal Equilibrium and The Zeroth Law of Thermodynamics
Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium.
The zeroth law of thermodynamics says that if two objects are each in equilibrium with a third object, they are also in thermal equilibrium with each other.

26. 17-4 Thermal Expansion
Linear expansion occurs when an object is heated.
Figure A thin rod of length l0 at temperature T0 is heated to a new uniform temperature T and acquires length l, where l = l0 + Δl.
Here, α is the coefficient of linear expansion.
T is the change in Temperature

27. 17-4 Thermal Expansion

28. 17-4 Thermal Expansion Example 17-3: Bridge expansion.
The steel bed of a suspension bridge is 200 m long at 20°C. If the extremes of temperature to which it might be exposed are -30°C to +40°C, how much will it contract and expand?
Solution: Substitution gives 4.8 cm expansion and 12 cm contraction.