AP Physics Chapter 14Sound

Chapter 14: Sound

14.1 Sound Waves14.2 The Speed of Sound14.3 Sound Intensity and Sound Intensity Level14.4 Sound Phenomena14.5 The Doppler Effect14.6 Musical Instruments and Sound

Characteristics

Homework for Chapter 14• Read Chapter 14

• HW 14.A: pp. 478-479: 10-15,18,28,29,30.

• HW 14.B: p. 480-481: 56, 57, 70, 74-78, 84, 85.

Warmup: Cheap Seats Physics Warmup #118

Modern baseball stadiums have a lot more to offer fans than the stadiums of decades past. One thing they still have in common, however, are the “cheap seats.” The back row of the upper deck will always be a long way from home plate. Not only is it hard to see what’s going on, it is even hard to hear what’s going on.

*********************************************************************************************Suppose you are sitting in your cheap seat and you decide to listen to the broadcast of the game on your pocket radio. When the first batter makes contact with the ball, you hear the crack of the bat through your radio earphones before you hear it in the ballpark! Explain why.

Answer: The radio transmission travels much farther but it travels at the speed of light. The actual sound wave travels through the ballpark air at the speed of sound.

14.1: Sound Waves

sound - the sensation produced when hearing vibrations transmitted through the air or other medium.

• Sound waves in fluids are primarily longitudinal (compressional) waves.

• Sound waves in solids can also have a transverse wave component.

• The high pressure regions of a sound wave are called condensations or compressions.

• The low pressure regions are called rarefactions.

• All sound waves are produced by vibrating sources such as human vocal cords or tuning forks.

A Tuning Fork as an Explanation of Sound

A tuning fork is basically a metal bar bent into a U-shape.

When struck, the prongs, or tines, vibrate with an antinode at the end of each tine.

The fork vibrates at its fundamental frequency, so a single tone is heard. A tone is a sound with a definite frequency.

As the fork vibrates, the compression waves propagate outward.

The pressure differences in the compression waves causes the eardrum to vibrate.

On the other side of the eardrum, tiny bones (the hammer, anvil, and stirrup) carry the vibrations to the inner ear.

The auditory nerve picks up the signal and carries it to the brain.

The Sound Frequency Spectrum

The audible region of sound for humans lies between about 20 Hz and 20 kHz.

infrasonic – frequencies below the range of human hearing.• Can be generated by earthquakes, wind, aircraft, automobiles, rapidly moving objects.

• Elephants and cattle may give early warnings of signs of earthquakes and weather disturbances.

ultrasonic - frequencies above the range of human hearing.

• Can be generated by high-frequency vibrations in crystals.

• Ultrasonic whistles can be used to call dogs.

Ultrasound Applications

Ultrasound is transmitted through tissue and is reflected from internal structures. The reflected waves are detected, and the signals are used to construct an image, or echogram, such as for a fetus.

Sonar is used for ranging and detecting. Sound pulses generated by sonar apparatus are reflected by underwater objects, and the resulting echoes are picked up by a detector. The time required for a sound pulse to make one round trip, together with the speed of sound in water, gives the distance of the reflecting object .

14.2: The Speed of Sound

• The speed of sound in a medium depends on the elasticity or the intermolecular interactions of the medium and the mass or density of its particles.

• Solids have more intermolecular interactions than liquids, and liquids more than gases.

• The speed of sound is generally 2 to 4 times faster in solids than in liquids and about 10 to 15 times faster in solids than in gases such as air.

Medium Speed (m/s)

Solids

Aluminum 5100

Copper 3500

Glass 5200

Liquids

Ethyl Alcohol 1125

Mercury 1400

Water 1500

Gases

Air (0°C) 331

Air (100°C) 387

Helium (0°C) 965

Hydrogen (0°C) 1284

Oxygen (0°C) 316

The Speed of Sound in Various Media

• The speed of sound depends on the temperature of the medium.

• The speed of sound in air increases with increasing temperature.

• For normal environmental temperatures, the speed of sound increases about 0.6 m/s for each degree Celsius above 0°C.

• A good approximation of the speed of sound in air for normal environmental temperatures is:

v = (331 + 0.6 Tc) m/s speed of sound in air

where Tc is the air temperature in degrees Celsius and331 m/s is the speed of sound in air at 0°C.

• A useful general value for the speed of sound in air is 1/3 km/s or 1/5 mi/s.

Example 14.1: The speed of an ultrasonic frequency 45 kHz in air is 342 m/s.

a)What is the air temperature?b)What is the wavelength of the sound wave?

Check for Understanding

1. A sound wave with a frequency of 15 Hz is in what region of the sound spectrum?

a) audible

b) infrasonic

c) ultrasonic

d) supersonic

Answer: b

Check for Understanding

2. A sound wave in air

a) is longitudinal

b) is transverse

c) has longitudinal and transverse components

d) travels faster than a sound wave through a liquid

Answer: a

Check for Understanding

3. The speed of sound is generally greatest in

a) solids

b) liquids

c) gases

d) a vacuum

Answer: a

Check for Understanding

4. Explain why sound travels faster in warmer air than in colder air.

Answer: Sound is a traveling disturbance like any other wave. The speed of the air molecules is greater in warmer air so the air molecules can pass the disturbance along faster.

Check for Understanding

5. The speed of sound in air

a) is about 1/3 km/s

b) is about 1/5 mi/s

c) depends on temperature

d) all of these

Answer: d

Check for Understanding

6.

Check for Understanding

6.

Warmup: Can You Hear Me Now? Physics Warmup #121

The loudness of sound can be measured in units called decibels (dB). The sound level of a person talking in a normal conversation is typically in the 60-dB range. Continued exposure to sound levels over 85 dB can cause permanent ear damage. People who work in loud environments, such as factories with large machines, are required to wear ear plugs.

*********************************************************************************************Modern technology has made it possible to play music in car stereos that far exceed 85 dB. Many teenagers spend significant amounts of money to raise the decibel level of their car stereos to 120 dB and beyond. As a result, some communities have passed laws limiting the sound level at which music can be played. Express your view on the need for such laws.

14.3: Sound Intensity and Sound Intensity Level

• intensity (I) is the rate at which power is transferred, per unit area.

I = energy/time = power area area

• The SI unit of intensity is W/m2.

• It is used most frequently with sound or light waves.

• The intensity is inversely proportional to the square of the distance from the point source.

• Therefore, intensity follows the inverse square law.

Question: What other physical phenomena follow the inverse square law? You may use your Gold Sheet to answer.

Answer: gravitational force, electric force

• The energy emitted from a point source spreads out equally in all directions.

• Since intensity is power/area I = P = P__ where the area is that of a spherical surface. A 4 R2

• The intensity then decreases with the distance from the source as 1 R2.

• Two intensities at different distances from a source of constant power can be compared as a ratio:

I2 = P/4 R22 = R1

2 I2 = R1 2

I1 = P/4 R12 = R2

2 or I1 R2

• Doubling the distance decreases the intensity to a quarter of its original value.

• Sound intensity is perceived by the ear as loudness.

• On the average, the human ear can detect sound waves (at 1 kHz) with an intensity as low as Io = 10-12 W/m2. This is called the threshold of hearing.

• At an intensity of Ip = 1.0 W/m2 sound is uncomfortably loud and may be painful to the ear. This is called the threshold of pain.

• The ratio between the two intensities Ip = 1.0 W/m2 = 1012. Io = 10-12 W/m2

• For a sound to be audible, it must have a frequency between 20 Hz and 20 kHz, and have an intensity greater than Io.

• Perceived sound is loudness is not directly proportional to intensity.

• Doubling the perceived loudness corresponds to an approximate increase in intensity by a factor of 10.

example: A sound with an intensity of 10-5 W/m2 would be perceived to be twice as loud as one with an intensity of 10-6 W/m2.

Sound Intensity Level – The Decibel

(threshold of hearing)

• At the threshold of hearing, I = Io, so, = 10 log Io = 10 log 1 = 0 dB Io

• At the threshold of pain, = 10 log 1.0 W/m2 = 10 log 1012 = 10 (12) = 120 dB Io

• The 12 orders of magnitude of sound intensity is only a difference of 120 dB – 0 dB = 120 dB, on the decibel scale.

Sound Intensity Levels and the Decibel Scale

Sound intensity and sound intensity level are two very different things.

• Intensity is a direct way to measure energy and is additive.

example: The sum of a 1.0 W/m2 sound and a 2.0 W/m2 sound will result in a sound of intensity 1.0 W/m2 + 2.0 W/m2 = 3.0 W/m2.

• Intensity level is based on a logarithmic scale and therefore is not additive.

example: The sum of a 10 dB sound and a 20 db sound will NOT make a sound of 10 dB + 20 dB 30 dB.

Example 14.3: Mrs. Pizarchik’s lecturing voice has a power of about 0.50 mW. If this power is assumed to be uniformly distributed in all directions,

a)What is the sound intensity at a distance of 5.00 m from her?

b) If you double the distance between you and the instructor, what is the new sound intensity?

c) What is the new sound intensity if you are 5.00 m apart and she raised her voice to double her power output?

Check for Understanding

1. If the air temperature increases, would the sound intensity from a constant output point source

a) increaseb) decreasec) remain unchanged

Answer: c

2. The decibel scale is referenced to a standard intensity of

a) 1.0 W/m2

b) 10-12 W/m2

c) normal conversationd) the threshold of pain

Answer: b

Check for Understanding

3. When sound passes from air into watera) its wavelength does not changeb) its frequency does not changec) its velocity does not changed) all of the above are true

Answer: b

4. As the temperature of the air increases, what happens to the velocity of sound? (Assume that all other factors remain constant.)a) It increases.b) It decreases.c) It does not change.

Answer: a

Homework for Chapter 14.1-3

• HW 14.A: pp. 478-479: 10-15,18,28,29,30.

Warmup:

Run the sound simulation.

http://phet.colorado.edu/en/simulation/sound

14.4: Sound Phenomena

• Since sound is a wave, it has wave characteristics. It can be:

reflected – waves bounce off objects or surfaces

refracted – waves change direction due to a medium or density change. •Temperature causes differences in air density.

diffracted – waves bend around corners, spread out beyond openings, or around objects.

•The object needs to be small compared to the wavelength.• Large wavelength, low frequency sounds diffract the most.

• Sound waves interfere when they meet.

constructive interference – two crests or two troughs coincide; in phase

destructive interference – a crest and a trough coincide; out of phase

Reflection of Sound

• The reflection of sound follows the law "angle of incidence equals angle of reflection", sometimes called the law of reflection. The same behavior is observed with light and other waves, and by the bounce of a billiard ball off the bank of a table.

• The reflected waves can interfere with incident waves, producing patterns of constructive and destructive interference. This can lead to resonances called standing waves in rooms. It also means that the sound intensity near a hard surface is enhanced because the reflected wave adds to the incident wave, giving a pressure amplitude that is twice as great in a thin "pressure zone" near the surface.

Refraction of Sound •Sound propagates in all directions from a point source. Normally, only that which is initially directed toward the listener can be heard, but refraction can bend sound downward.

• Normally, only the direct sound is received. But refraction can add some additional sound, effectively amplifying the sound.

• Natural amplifiers can occur over cool lakes.

Diffraction of Sound

Diffraction of Sound

The long wavelength sounds of the bass drum will diffract around the corner more efficiently than the more directional, short wavelength sounds of the higher pitched piccolo.

Interference

• Sound waves from two point sources spread out and interfere.

• At points where they arrive in phase (zero phase difference), constructive interference occurs.

• At points where the waves arrive completely out of phase (phase difference of 180°), destructive interference occurs.

• The phase difference at a particular point depends on the path lengths the waves travel to reach that point.

http://www.falstad.com/interference/

Interference Simulation

Check for Understanding

1.

Check for Understanding

2.

Check for Understanding:

3. As a person walks between a pair of loudspeakers that produce tones of the same amplitude and frequency, he hears a varying sound intensity. Explain.

Answer: The varying sound intensity is caused by the interference effect. At certain locations there is constructive interference and at other locations, there are destructive interference.

Warmup: Did You Hear What I Saw? Physics Warmup #119

Lightning and thunder are created at the same time by the same event. The speed of light is 186,000 miles per second, while the speed of sound in air is typically around 700 miles per hour. As a result, you see the lightning before you hear the thunder.

*********************************************************************************************You might have heard the old rule of thumb that every five seconds that elapse between seeing the lightning and hearing the thunder represents one mile of distance between you and the lightning. Use the speeds of light and sound to check the accuracy of that statement.

Answer: Yes!

time for light to travel 1 mile:t = d = 1 mile = 5.4 x 10-6 s (instantaneous) v 186,000 mi/s

time for sound to travel 1 mile:700 mi/hr = 0.194 mi/st = d = 1 mi = 5.1 seconds v 0.194 mi/s

14.5: The Doppler Effect

The Doppler Effect

• If there is relative motion between a sound source and an observer, the observer will detect a frequency which is different from the frequency of the source.

• This phenomena is called the Doppler effect. It is named after the Austrian physicist, Christian Doppler (1803-1853) who first described the effect.

• Generally, if the source and the observer are moving toward each other, the observed frequency is higher than the source frequency.

• If the source and the observer are moving away from each other, the observed frequency is lower than the source frequency.

View Applet: http://www.loncapa.org/~mmp/applist/doppler/d.htm

The Doppler Effect

Sound waves bunch up in front of a moving source – the whistle- giving a higher frequency there. They trail out behind the source, give a lower frequency there.

The pitch is the perceived frequency.

Applications of the Doppler Shift

radar (radio detecting and ranging)Radio waves are emitted, reflected, and recaptured by the gun. If your car is moving towards the patrol car, the reflected waves have a higher frequency. The Doppler shift depends on the speed. A computer calculates the speed and displays it for the police officer.

Doppler radarDoppler radar can measure the Doppler frequency shift in addition to the magnitude of the echo signal reflected from precipitation. The Doppler shift is related to the velocity of the precipitation blown by wind either toward or away from the radar installation.

The Doppler Effect for Light Waves

When a distant light source moves away from us, the frequency of the light we receive from it is lowered. Light is shifted toward the red (long-wavelength) end of the spectrum, known as the Doppler red shift.

Similarly, the frequency of light from an object approaching us is increased, and light is shifted toward the blue (short wavelength) end of the spectrum. This produces Doppler blue shift.

The amount of frequency shift depends on the speed of the source.

The Doppler shift of light from astronomical objects is very useful to astronomers. For example, in this picture the velocity of the Sun’s corona is mapped as plasma moves toward (blue shifted) or away from (red shifted) the satellite which is capturing data.

Check for Understanding:

1.Is there a Doppler effect if a sound source and an observer are moving with the same velocity?

Answer: No. There is no relative velocity between the observer and the source.

2. What would be the effect if a moving source accelerated toward a stationary observer?

Answer: An increasing sound frequency is observed since the source is moving toward the observer and its speed increases.

Check for Understanding:

3. Astronomers have observed that all distant galaxies appear red-shifted. Is this evidence for an expanding, contracting, or stationary universe?

Answer: Expanding, because red shift indicates they are moving away from each other.

Check for Understanding:

4. Traffic radar is based on

a) beats

b) the Doppler effect

c) interference

d) refraction

Answer: b

Davy Jones Plays His Pipe Organ

http://www.youtube.com/watch?v=L0JbaZtoKAs

14.6: Musical Instruments and Sound Characteristics

• Musical instruments provide good examples of standing waves and boundary conditions.

• Example: a guitar. For a stretched string, fixed at each end, the natural frequencies are

fn = n(v/2L) = nf1 (for n = 1,2,3…)where v is the velocity of the waveL is the length of the string

• The velocity of the wave on the string depends on the tension and inertia of the string.

• The effective length of the string is varied by finger location and pressure.

• The natural frequencies for pipes (where v is the speed of sound in air) are

fn = v/n = n(v/2L) = nf1 (for n = 1,2,3…) pipe open on both ends

fm = v/m = m(v/4L) = mf1 (for m = 1,3,5…) pipe closed on one end

Open organ pipe Closed organ pipe

Organ Pipes

• Standing waves can also be set up in wind instruments, such as the organ pipe.

• Pipe organs have fixed length pipes which may be opened or closed.

• Longitudinal standing waves are formed in vibrating air columns in pipes.

• An open pipe has antinodes at both ends.

• A closed pipe has a closed (node) end and an open (antinode) end.

• To solve problems with pipes, always begin withthe length of the pipe. If it is open at both ends, the biggest wave that can fit the pipe has a wavelength twice the pipe’s length. If it is closed atone end, the biggest wave is four times longer thanthe pipe.

Example 14.9: A 3.00 m long pipe is in a room where the temperature is 20°C. a)What is the fundamental frequency if the pipe is open?b)What is the frequency of the second harmonic if the pipe is open?c)What is the fundamental frequency if the pipe is closed?d)What is the frequency of the second harmonic of the pipe is closed?

beats - rhythmic interference that occurs when two notes of unequal but close frequencies are played.

Two traveling waves of equal amplitude and slightly different frequencies interfere and give rise to pulsating tones called beats. The listener will hear these beats at a

beat frequency: fb = f1 - f2

https://www.youtube.com/watch?v=eVIKrAdpuqU

Example 14.6: A music tuner uses a 256 Hz tuning fork to tune the frequency of sound from a musical instrument. It the tuner hears a beat frequency of 2.0 Hz, what is the frequency of the sound produced by the instrument?

Check for Understanding:

1.When you blow across the top of a bottle with water in it, why does the frequency of the sound increase with increasing levels of water?

Answer: As the level of water increases in the bottle, the length of the air column above the water decreases. This decrease in length of the air column decreases the wavelength and increases the frequency.

Check for Understanding:

2. Beats are a direct result of

a) interference

b) refraction

c) diffraction

d) the Doppler effect

Answer: a

Check for Understanding:

3. Traffic radar is based on

a) beats

b) the Doppler effect

c) interference

d) refraction

Answer: b

Check for Understanding:

4.

Homework for Chapter 14.4-6

• HW 14.B: p. 480-481: 56, 57, 70, 74-78, 84, 85.