Sound Waves Dancing Liquids A sound wave is introduced into a medium by the vibration of an object. Sound is a longitudinal, mechanical wave. For example, a guitar string forces surrounding air molecules to be compressed and expanded, creating a pressure disturbance consisting of an alternating pattern of compression and rarefactions. The disturbance then travels from particle to particle through the medium, transporting energy as it moves. The amount of energy which is transferred to the medium is dependent upon the amplitude of vibrations of the guitar sting. compression rarefaction 1
The Speed of Sound in Air The speed of sound in air is 331 plus the product of 0.59 and the Celsius temperature. v = 331 + 0.59T c Example Suppose the temperature of the classroom is 21 o C. Calculate the speed of sound in the classroom. 2
The Speed of Sound in Solids and Liquids In general, sound travels the fastest in solids, slower in liquids and slowest in gases. Examples Material Speed (m/s) Gases carbon dioxide 259 oxygen 316 Liquids fresh water 1482 seawater 1440 1500 (depends on depth and salinity) Gases copper 5010 steel 5960 The speed of sound in water is almost five times faster than its speed in air. This difference is great enough to be noticed by the human ear. A swimmer who is 1500 m away from a loud noise would hear the sound that travelled through the water 1 s after is was produced. The same sound travelling through air, however, would not be heard until 5 s after it was produced. 3
P11 Waves 2 Sound.notebook December 09, 2013 Pitch, Loudness and Quality In humans, sound is detected by the ear and interpreted by the brain. Sound characteristics are defined in terms describing what we perceive. Sounds varies in pitch (perceived frequency). The words high and low to describe the frequency of a sound. The human hear responds to sounds in the audible range: 20 Hz to 20 000 Hz A sound whose pitch is below 20 Hz is referred to as infrasonic. Elephants communicate using infra sonic sounds. Infrasonic sounds can be created by machinery and earthquakes. A sound whose pitch is above 20 000 Hz is referred to as ultrasonic. Dolphins communicate using ultra sonic sounds. Most species of bats are able to "see" using ultrasonic sounds, enabling them to catch their prey in the dark. Sounds vary in loudness (perceived intensity). Jet aircraft engines are so loud that airport workers have to wear ear protection. The breathing of a sleeping baby is very quiet. Kermit and Elmo Loud and Quiet 4
Sounds also vary in another important way called quality. It is the quality of a sound that enables you to identify it as being made by a piano rather than a trumpet, even when the two instruments play notes at the same loudness and pitch. Pure sounds are produced by sources vibrating at only one natural frequency. The sound of a flute or whistle is described as pure. A rich sound is heard when a source vibrates at several of its natural frequencies at the same time. The sound of a cello or organ is described as rich. 5
A noise is a mixture of many sound frequencies with no recognizable relationship to each other. Music is a mixture dominated by sound frequencies known as harmonics that are whole number multiples of the lowest frequency or the fundamental frequency. 6
Sound waves reflect, refract, diffract and interfere. Reflection The reflection of a sound wave is called an echo. Bats and dolphins use a process called echolocation. They are able to generate and interpret ultrasonic pulses that reflect off obstacles and prey. Refraction Instead of changing direction suddenly at the boundary between two media, the direction of sound changes gradually as it passes through air of differing temperatures. Lightening superheats the air. As sound travels faster in warmer air, the sound of thunder is refracted upward away from the surface of Earth. Diffraction You will hear a siren long before you see a fire truck, because sound can bend around corners. 7
Interference When two sound waves of very similar, but not identical, frequencies interfere with one another a special phenomenon occurs. Beats are produced by alternating instances of constructive and destructive interference over time. You will hear the intensity of the sound wavering from loud to soft and back to loud. (Beat Loaf) One beat is a complete cylce from loud to soft to loud. 8
The superposition of two similar waves produces a resultant sound wave with an intensity that alternates between loud and soft. The beat freqency is the absolute value of the difference of the frequencies of the two component waves. 9
Sample Problems 1. Two tuning forks are struck at the same time. One has a frequency of 548 Hz and the other a freqeuncy of 542 Hz. What is the beat frequency? 548 HZ 542 Hz 2. One tuning fork has a frequency of 256 Hz. When it and another tuning fork are struck at the same time, a beat frequency of 4 Hz is heard. What is the frequency of the second tuning fork? 10
Intensity and the Decibel Scale The amount of energy that is transported past a given area of the medium per second is known as the intensity of the sound wave. The greater the amplitude of vibrations of the particles of the medium, the greater the rate at which energy is transported through it, and the more intense the sound wave will be. Intensity = Energy = Power Time Area Area The units of intensity are watts/meter 2 (W/m 2 ). The human ear can normally hear intensities as small as 1.0 x10 12 W/m 2 to as large as 1 W/m 2. This is a HUGE range of intensities. The threshold of hearing, I o, is the minimum sound intensity that the average human can hear. It has an intensity of 1.0 x 10 12 W/m 2. 11
Since the range of intensities which the human ear can detect is so large, physicists use a scale based on powers of 10. It is called the decibel scale. The threshold of hearing is assigned a sound level of 0 db. IMPORTANT If one sound is 10 x times more intense than another, then it has a sound level which is 10x more decibels than the less intense sound. 12
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Sample Problems 1. How many times more intense is a 50 db sound as compared to a 30 db sound? 2. How many times more intense is a 70 db sound compared to a 60 db sound? 3. How many times more intense is a 120 db sound compared to a 90 db sound? 4. The sound level of sound A is 50 db. If sound B is 100 000 times as intense, what is its sound level? 5. The sound level of sound A is 10 db. If sound B is 100 times as intense, what is its sound level? 14
How do we convert intensities which are measured in W/m 2 to decibels? We use the following formula! β is the intensity level measured in db log is the logarithmic function I is the intensity of the sound in question in W/m 2 I o is the intensity of the threshold of hearing I o = 1.0 x 10 12 W/m 2 The whole point of using the log function is that it shrinks the huge range of intensities down to a reasonable range of sound levels. 15
Sample Problem 1. What is the sound level of a sound whose intensity is 1.00 x 10 9 W/m 2? 1.00 x 10 9 W/m 2 β? I 1.00 x 10 9 W/m 2 I o 1.0 x 10 12 W/m 2 1.0 x 10 12 W/m 2 2. What is the sound level of a sound whose intensity is 5.00 x 10 6 W/m 2? β? I 5.00 x 10 6 W/m 2 5.00 x 10 6 W/m 2 I o 1.0 x 10 12 W/m 2 1.0 x 10 12 W/m 2 3. What is the sound level of a sound whose intensity is 3.68 x 10 4 W/m 2? 1.0 x 10 12 W/m 2 16
Doppler Effect Have you ever noticed how the sound of an emergency vehicle's siren seems to increase in pitch as it approaches? Then, just as the vehicle passes, the pitch suddenly appears to drop? The phenomenon responsible for the apparent change in the pitch is called the Doppler effect. The siren generates exactly the same sound at all times. The apparent changes in pitch as the vehicle approaches, then recedes, results from the motion of the vehicle as the source of sound. The frequency of approaching car's siren goes up when the sound moves toward an observer and down when it moves away from the observer. NOTE The frequency of the car's siren does not change when you are traveling at the same speed as the source. 17
How do we calculate the Doppler shift for sound waves? Why, we use the following formula! observed frequency in Hz f frequency of the source in Hz v speed of sound (usually 343 m/s) v o velocity of the observer in m/s v s velocity of the sound source in m/s HINT If the distance between the source and observer decreases, use ±. If the distance between the source and observer increases, use. 18
Sample Problems 1. A man on a train, which is traveling at 34.0 m/s, listens to a stationnary siren that has a frequency of 3.60 x 10 2 Hz. What frequency does the man hear as the train approaches the siren?? f 3.60 x 10 2 Hz v speed of sound (usually 343 m/s) v o 34.0 m/s v s 0 = 3.60 x 10 2 Hz The man hears a frequency of 3.96 x 10 2 Hz as the train approaches the siren. 19
2. A car's engine hums with a frequency of 2.50 x 10 2 Hz. The car approaches and then passes you. What frequency will you hear as the car moves away from you at 20.0 m/s? f v v o v s? 2.50 x 10 2 Hz speed of sound (usually 343 m/s) 0 m/s 20.0 m/s You will hear the car at a frequency of 2.26 x 10 2 Hz as the car moves away from you. 20
3. A locomotive leaves a railroad crossing at 75.0 km/h while sounding its whistle. The whistle has a frequency of 425 Hz. As the locomotive moves away from the crossing, what is the frequency heard by a boy standing at the crossing? 21
4. As you drive down the highway at a constant speed of 20.0 m/s, an ambulance, with a 365 Hz siren wailing, approaces you from behind at a constant speed of 32.0 m/s. What frequency do you hear as the ambulance gets closer? 22
Sample Problems - Beats 1. Two tuning forks are struck at the same time. One has a frequency of 548 Hz and the other a freqeuncy of 542 Hz. What is the beat frequency? 548 HZ 542 Hz 2. One tuning fork has a frequency of 256 Hz. When it and another tuning fork are struck at the same time, a beat frequency of 4 Hz is heard. What is the frequency of the second tuning fork? Sample Problems - Intensity 1. How many times more intense is a 50 db sound as compared to a 30 db sound? 2. How many times more intense is a 70 db sound compared to a 60 db sound? 3. How many times more intense is a 120 db sound compared to a 90 db sound? 4. The sound level of sound A is 50 db. If sound B is 100 000 times as intense, what is its sound level? 5. The sound level of sound A is 10 db. If sound B is 100 times as intense, what is its sound level? 23
Sample Problems - Intensity Equation 1. What is the sound level of a sound whose intensity is 1.00 x 10 9 W/m 2? 2. What is the sound level of a sound whose intensity is 5.00 x 10 6 W/m 2? 24
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Check Your Understanding Which of the following is NOT a property of sound? a. Amplitude b. Frequency c. Mass d. Wavelength 27
Check Your Understanding When the amplitude of a sound wave increases, a. The wavelength of sound decreases b. The sound gets louder c. The pitch increases d. The speed of sound increases Sound in a longitudinal wave because a. the oscillations in pressure are in the same direction as the wave moves. b. The oscillations in pressure are perpendicular to the direction that the wave moves. c. The wavelength is long compared to light waves. d. The wavelength is always longer than the amplitude. 28
Check Your Understanding The wavelength of a sound wave can be calculated by a. Multiplying the amplitude by the frequency b. Dividing amplitude by frequency c. Multiplying speed by frequency d. Dividing speed by frequency The speed of sound in air at 7.0 is a. 331 m/s b. 332 m/s c. 335 m/s d. 338 m/s 29
Check Your Understanding A person behind an ambulance as it moves away from her. The pitch of the sound that she hears is a. Lower than if the ambulance was stationary. b.the same as if the ambulance was stationary. c. Higher than if the ambulance was stationary. 30
Module Summary In this module you learned that Sound waves are longitudinal mechanical waves. Sounds can be distinguished by loudness and pitch. When two frequencies are close but not the exact same, beats will be heard with a frequency of Sound travels through air with a speed given by The Doppler Effect can be explained using wave theory and that frequency as a result of the Doppler Effect can be calculated using 31
Attachments Dancing Liquids