Warm-Up: February 29, 2016 Write down everything you know about sound.

Homework Questions?

Think-Pair-Share If a tree falls in the woods and no one is around to hear it, does it make a sound? In space, can anyone hear you scream?

Chapter 15 (OpenStax Chapter 17) Sound Chapter 15 (OpenStax Chapter 17)

Sound and Hearing Sound is a disturbance of matter that is transmitted outward from its source. Sound is a wave. Hearing is the perception of sound, just as vision is the perception of light.

Vibrating String As a string vibrates, a small portion of its energy goes into compressing and expanding the surrounding air. These compressions (high pressure regions) and rarefactions (low pressure regions) move out as longitudinal waves having the same frequency as the string.

Sound Waves Longitudinal in air and most other fluids. In solids, can be both transverse and longitudinal. Amplitude of sound waves decrease with distance from its source. Spread out over larger and larger areas. Absorbed by objects (including eardrums). Energy lost as heat. Wavelength, frequency, amplitude, and speed are important, as they are for all waves.

Frequency Same as for other waves. Perception of frequency is called pitch.

Still true

You-Try #2 What frequency sound has a 0.10 m wavelength when the speed of sound is 340 m/s?

Wavelength Distance between adjacent identical parts.

Solids (longitudinal) Speed of Sound Depends on temperature. Higher temperature  faster particle motion  faster sound waves Nearly independent on frequency or wavelength Sample speeds, in m/s Gases at 0°C Liquids at 20°C Solids (longitudinal) Air 331 Ethanol 1160 Polyethalene 920 CO2 259 Mercury 1450 Marble 3810 Oxygen 316 Fresh water 1480 Glass (Pyrex) 5640 Helium 965 Sea water 1540 Lead 1960 Hydrogen 1290 Human tissue Steel 5960

Speed of Sound Table 15-1, Page 405 (Need for homework) (Do not need to memorize – a table will be provided on your test)

Warm-Up: March 1, 2016 A sonar echo returns to a submarine 1.20 s after being emitted. What is the distance to the object creating the echo? Assume the submarine is stationary in the ocean.

Reminder Units Quiz next class All or nothing

Changing Medium The medium is the matter through which a sound wave travels. When a sound wave passes from one medium to another, frequency and period stay constant. Wave speed is determined by the medium (and temperature). Wavelength is determined by

Think-Pair-Share You observe two musical instruments that you cannot identify. One plays high-pitch sounds and the other plays low-pitch sounds. How could you determine which is which without hearing either of them play? Solution: Compare their sizes. High-pitch instruments are generally smaller than low-pitch instruments because they generate a smaller wavelength.

You-Try #10 A physicist at a fireworks display times the lag between seeing an explosion and hearing the sound, and finds it to be 0.400 s. His thermometer shows an air temperature of 20.0°C. Estimate the distance between the physicist and the explosion.

Sound Intensity and Sound Level OpenStax Section 17.3

Sound Intensity The “loudness” of a sound depends on its sound intensity, 𝐼. Intensity= Power Area = ∆pressure 2 2𝜌 𝑣 𝑤 (Do not need to memorize) SI unit is 𝑊 𝑚 2 Sound intensity level, 𝛽, is measured in decibels The bel, upon which the decibel is based, is named for Alexander Graham Bell 𝛽 dB =10 log 10 𝐼 +120 (Do not need to memorize) Logarithmic scale

Sound Intensity Level, 𝜷 (dB) Intensity, 𝑰 (W/m2) Example/effect 1× 10 −12 Threshold of hearing at 1000 Hz 10 1× 10 −11 Rustle of leaves 20 1× 10 −10 Whisper at 1 m distance 30 1× 10 −9 Quiet home 40 1× 10 −8 Average home 50 1× 10 −7 Average office, soft music 60 1× 10 −6 Normal conversation 70 1× 10 −5 Noisy office, busy traffic 80 1× 10 −4 Loud radio, classroom lecture 90 1× 10 −3 Inside a heavy truck; Damage from prolonged exposure 100 1× 10 −2 Noisy factory, siren at 30 m; Damage from 8 h/day exposure 110 1× 10 −1 Damage from 30 min/day exposure 120 1 Loud rock concert; Threshold of pain 140 1× 10 2 Jet airplane at 30 m; Severe pain, damage in seconds 160 1× 10 4 Bursting of eardrums

Relationships between 𝐼 and 𝛽 Double 𝐼  𝛽 increases by 3 dB Multiply 𝐼 by 5  𝛽 increases by 7 dB Multiply 𝐼 by 10  𝛽 increases by 10 dB

Doppler Effect and Sonic Booms OpenStax Section 17.4

Doppler Effect The Doppler Effect is an alteration of the observed frequency of a sound due to motion of either the source or the observer. The change in frequency due to relative motion is called a Doppler shift. Named after Austrian Christian Johann Doppler (1803-1853)

Stationary Source, Stationary Observer

Moving Source, Stationary Observer

Stationary Source, Moving Observer

Doppler Effect Occurs for all waves, including sound, light, and water waves. Used to determine relative velocities of galaxies. (See Page 408 of your textbook for special cases of the equation.)

You-Try 17.4 Suppose a train that has a 150. Hz horn is moving at 35.0 m/s in still air when the speed of sound is 340. m/s. What frequencies are observed by a stationary person at the side of the tracks as the train approaches and after it passes? What frequency is observed by the train’s engineer traveling on the train?

Suppose a train that has a 150. Hz horn is moving at 35 Suppose a train that has a 150. Hz horn is moving at 35.0 m/s in still air when the speed of sound is 340. m/s. What frequencies are observed by a stationary person at the side of the tracks as the train approaches and after it passes? What frequency is observed by the train’s engineer traveling on the train?

Warm-Up: March 2/3, 2016 The frequency of the middle C musical note is 261.63 Hz. A cello plays a middle C inside in a house where the air temperature is exactly 20℃. What is the period of the sound wave? What is the wavelength of the sound wave? The sound wave travels out of the house through an open window. If the temperature of the air outside is exactly 0℃, what are the frequency, period, and wavelength of the sound wave outside?

Homework Questions?

Sonic Booms As 𝑣 source approaches 𝑣 sound , 𝑓 obs approaches infinity When 𝑣 source = 𝑣 sound , the front edge of each successive wave is superimposed on the previous one. The observer gets them all at the same instant, so 𝑓=∞, but only if the observer is directly in the path of the object. Not considered a sonic boom. A sonic boom is created when 𝑣 source > 𝑣 sound , where maximum superposition of sound waves is along a cone with the moving object at the tip of the cone

Sonic Boom

Sonic Boom Object traveling faster than speed of sound. No sound is received by the observer until after the object passes. Sound waves from approaching source are superimposed with sound waves from the receding object. Constructive interference creates a cone-shaped shock wave, called a sonic boom.

Sonic Boom

Two sonic booms from one airplane

Mach Number

Bow Wakes A bow wake is created when the wave source moves faster than the wave propagation speed. A sonic boom is an example of a bow wake.

Think-Pair-Share What are some applications of the Doppler Effect?

Applications of Doppler Shift Ultrasound – measure blood velocity Police radar – measure car velocities Meteorology – track storm clouds Astronomy – relative speeds of galaxies

You-Try 36 Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s. Both screech, the first one emitting a frequency of 3200 Hz, and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?

Assignment Read Section 15.1 Optional: Read OpenStax 17.1-17.4 Page 405 #1-5; Page 409 #6-10; Page 410 #12-17 Read Section 15.2

Units Quiz! Clear everything off of your desk except writing utensils and erasers. 8 minute time limit If you appear to be talking, looking at anyone else’s quiz, allowing another student to look at your quiz, or using any unauthorized aide, you will receive a zero. If any electronic device is seen or heard, it goes to the office and you will receive a zero.

The Physics of Music Section 15.2

Sound Interference and Resonance: Standing Waves in Air Columns OpenStax Section 17.5

Sound Interference All waves exhibit constructive and destructive interference. Demonstrating interference proves something is a wave. Noise-cancelling technology uses destructive interference to reduce noise levels by 30 dB or more. Sound resonance, such as in musical instruments, is due to interference.

Beats When two sound waves of similar frequencies interfere, beats are generated. 𝑓 𝐵 = 𝑓 2 − 𝑓 1

You-Try 40 What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?

Resonance in Tubes Resonant frequencies interfere constructively. Other frequencies interfere destructively and are absent. Half-open tube (open at one end, closed at the other) Sound wave enters the open end of the tube. Sound wave travels down the tube. Sound wave reflects off the closed end. Sound wave return to the open end. If the wavelength of the sound wave and the length of the tube are correct, the exiting sound wave constructively interferes with the incoming sound wave, and a standing wave is created. An antinode (maximum displacement) at the open end A node (no displacement) at the closed end

Figure 17.23 Resonance of air in a tube closed at one end, caused by a tuning fork. A disturbance moves down the tube.

Figure 17.24 Resonance of air in a tube closed at one end, caused by a tuning fork. The disturbance reflects from the closed end of the tube.

Figure 17.25 Resonance of air in a tube closed at one end, caused by a tuning fork. If the length of the tube L is just right, the disturbance gets back to the tuning fork half a cycle later and interferes constructively with the continuing sound from the tuning fork. This interference forms a standing wave, and the air column resonates.

Figure 17.26 Resonance of air in a tube closed at one end, caused by a tuning fork. A graph of air displacement along the length of the tube shows none at the closed end, where the motion is constrained, and a maximum at the open end. This standing wave has one-fourth of its wavelength in the tube, so that λ = 4L .

Fundamental Frequency Any wavelength that produces a node at the closed end and an antinode at the open end will produce a standing wave. The longest possible wavelength is 𝜆=4𝐿, where 𝐿 is the length of the pipe. This creates the lowest possible frequency, called the fundamental frequency.

Overtones Instead of one-fourth of a wavelength fitting inside the tube, 3/4 or 5/4 or 7/4, etc. could fit inside the tube. These shorter wavelengths create higher frequency standing waves called overtones.

Harmonics Harmonics include the fundamental frequency and all overtones. The first harmonic is the fundamental frequency The second harmonic is the first overtone The third harmonic is the second overtone

Harmonics The fundamental and overtones can be present in a variety of combinations. This is why middle C sounds different on different instruments. The fundamental frequency is the same, but the overtones and their mix of intensities are different.

Warm-Up: March 4, 2016 A rock is dropped down a well on a warm summer day. A splash is heard 2.35 seconds later. How far below the top of the well is the water? Use 𝑔=9.80 m/s2.

Tube closed at one end Resonant frequencies of a tube closed at one end are 𝑓 1 is the fundamental 𝑓 3 is the first overtone …

You-Try 17.5 What length should a tube closed at one end have on a day when the air temperature is 22.0℃ 𝑣 𝑤 =344 m s , if its fundamental frequency is to be 128 Hz (C below middle C)? What is the frequency of its fourth overtone?

What length should a tube closed at one end have on a day when the air temperature is 22.0℃ 𝑣 𝑤 =344 m/s , if its fundamental frequency is to be 128 Hz? What is the frequency of its fourth overtone?

You-Try 48a Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when the speed of sound is 342 m/s.

Tube open at both ends Resonance is created with antinodes (maximum displacement) at both ends. Resonant frequencies of a tube open at both ends are: 𝑓 1 is the fundamental 𝑓 2 is the first overtone 𝑓 3 is the second overtone

You-Try 44 What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this, because of its double reed.)

Assignment Read Section 15.2 Optional: Read OpenStax Section 17.5 Page 424 #30-39 all, 53-61 odd, 71-79 odd