# Physical Science Waves Slides subject to change. Energy Transfer A wave is a disturbance that propagates through space and time. A wave is a disturbance.

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Physical Science Waves Slides subject to change

Energy Transfer A wave is a disturbance that propagates through space and time. A wave is a disturbance that propagates through space and time. Waves transfer energy. Waves transfer energy. Sinking rock does work pushing surface water aside. Energy transferred to water. Sinking rock does work pushing surface water aside. Energy transferred to water. Water surface molecules push nearby molecules... Water surface molecules push nearby molecules... Wave “propagates” through the water. Wave “propagates” through the water.

Longitudinal Wave Longitudinal wave: Particles move in same direction as the wave. Longitudinal wave: Particles move in same direction as the wave. Examples: Sound waves, “Slinky” spring. Examples: Sound waves, “Slinky” spring. Animation courtesy of Dr. Dan Russell, Kettering University

Transverse Wave Transverse wave: Particles move perpendicular to wave direction. Transverse wave: Particles move perpendicular to wave direction. Examples: Electromagnetic waves (radio, television, optical), waves on a string. Examples: Electromagnetic waves (radio, television, optical), waves on a string. Animation courtesy of Dr. Dan Russell, Kettering University

Wave Properties A medium propagates waves. A medium propagates waves. Amplitude is the maximum displacement from equilibrium. Amplitude is the maximum displacement from equilibrium.

Period Period (T ), is the time between successive peaks. Period (T ), is the time between successive peaks. Time t Period time →

“Period” is the time between successive peaks (or wave crests).

Frequency Frequency is the rate at which peaks are arriving. Frequency is the rate at which peaks are arriving. Units are generally events per time, such as revolutions per minute. Cycles per second units are called Hertz (Hz). Units are generally events per time, such as revolutions per minute. Cycles per second units are called Hertz (Hz). Examples Examples Surfer waves: 4 crests per minute. Surfer waves: 4 crests per minute. Electrical Outlet: 60 Hz Electrical Outlet: 60 Hz

Music Music “middle C” 262 Hz (cycles per second). Music “middle C” 262 Hz (cycles per second).

Relate Period and Frequency If middle C is 262 Hz, what is the time between crests? If middle C is 262 Hz, what is the time between crests? Given Formula Given Formula f = 262 Hzf = 1/T f = 262 Hzf = 1/T therefore, 262 = 1/T, T = 0.0038 seconds therefore, 262 = 1/T, T = 0.0038 seconds f = 1/T

Wavelength Associated with a traveling wave. Associated with a traveling wave. Wavelength (λ) is the distance between successive crests. Wavelength (λ) is the distance between successive crests. Traveling Wave Traveling Wave Traveling Wave Traveling Wave

Wavelength is the distance between crests.

Sound The speed of sound is 344 m/s under standard conditions in air (sea level, 20 °C). The speed of sound is 344 m/s under standard conditions in air (sea level, 20 °C). That’s about 768 mph. That’s about 768 mph. Wave speed = wavelength times frequency Wave speed = wavelength times frequency v = λ f

Wavelength If the frequency of a concert tone is 262 Hz, what is the wavelength λ? If the frequency of a concert tone is 262 Hz, what is the wavelength λ? GivenFormula v = 344 m/sv = λ f v = 344 m/sv = λ f f = 262 Hz f = 262 Hz v = λ f v = λ f 344 = λ(262) 344 = λ(262) λ = 1.31 m λ = 1.31 m

Electromagnetic Waves The wave, or "disturbance," is a transverse electric field, which is invisible. Causes charged particles to move. The wave, or "disturbance," is a transverse electric field, which is invisible. Causes charged particles to move. Light, microwaves, x-rays, TV, and radio transmissions are various kinds of electromagnetic waves. Light, microwaves, x-rays, TV, and radio transmissions are various kinds of electromagnetic waves. The electric field interacts with electrons and protons. The electric field interacts with electrons and protons.

Electromagnetic Waves Speed of light c = 3.0x10 8 m/s Speed of light c = 3.0x10 8 m/s KFI AM radio broadcasts at f = 640 kHz. What is the wavelength? KFI AM radio broadcasts at f = 640 kHz. What is the wavelength? GivenFormula GivenFormula v = 3.0x10 8 m/sv = λ f v = 3.0x10 8 m/sv = λ f f = 640 kHz = 640x10 3 Hz f = 640 kHz = 640x10 3 Hz 3x10 8 = λ (640x10 3 ) 3x10 8 = λ (640x10 3 ) λ = 470 m Radio wavelength is important in antenna design. λ = 470 m Radio wavelength is important in antenna design.

Sound Wave Characteristics Sound is propagation of compression waves through matter (solid, liquid, or gas). Sound is propagation of compression waves through matter (solid, liquid, or gas). Three regions. Three regions. Ultrasonic > 20,000 Hz (medicine, some animals – dogs, bats – can hear) Ultrasonic > 20,000 Hz (medicine, some animals – dogs, bats – can hear) Audible 20 Hz – 20,000 Hz, (human hearing) Age Test Audible 20 Hz – 20,000 Hz, (human hearing) Age Test Age Test Age Test Infrasonic < 20 Hz (earthquakes, some animals – cattle, elephants - can hear or feel?) Infrasonic < 20 Hz (earthquakes, some animals – cattle, elephants - can hear or feel?)

Intensity Measure intensity = rate of energy transfer through a given area (power/area = W/m 2 ). Measure intensity = rate of energy transfer through a given area (power/area = W/m 2 ). Sound Intensity Sound Intensity Minimum intensity human can hear is about 10 -12 W/m 2, the threshold of hearing... a mosquito at 10 feet! Minimum intensity human can hear is about 10 -12 W/m 2, the threshold of hearing... a mosquito at 10 feet! Intensity decreases the farther you are from the source. Goes as 1/r 2. Intensity decreases the farther you are from the source. Goes as 1/r 2.

Sound Loudness Loudness, in bels (after Alexander Grahm Bell), of a sound of intensity I is defined to be Loudness, in bels (after Alexander Grahm Bell), of a sound of intensity I is defined to be I 0 is the minimum intensity detectable by the human ear. I 0 is the minimum intensity detectable by the human ear.

Sound Loudness Logarithms are powers of 10. Logarithms are powers of 10. If a sound is 100 times more intense than another, its loudness is 2 bels more (factor of 100 or 10 2 ) If a sound is 100 times more intense than another, its loudness is 2 bels more (factor of 100 or 10 2 ) If one sound is 6 bel, and another is 9 bel, it is 1000 times more intense (10 3 ). If one sound is 6 bel, and another is 9 bel, it is 1000 times more intense (10 3 ).

Sound Loudness The bel is a large unit, so a sub-unit, the decibel, is generally used. The bel is a large unit, so a sub-unit, the decibel, is generally used. If one sound is 100 times louder than another, it is 2 bels or 20 dB louder. If one sound is 100 times louder than another, it is 2 bels or 20 dB louder.

Intensity Levels Think POWERS OF TEN Think POWERS OF TEN Threshold of hearing 0 dB, a mosquito 10 feet away. Threshold of hearing 0 dB, a mosquito 10 feet away. Humming of a refrigerator 40 db (10 4 · I 0 ) Humming of a refrigerator 40 db (10 4 · I 0 ) Conversation 60 dB (10 6 · I 0 ). Conversation 60 dB (10 6 · I 0 ). Leaf blower user 90 dB (10 9 · I 0 ). Leaf blower user 90 dB (10 9 · I 0 ). Rock band 110 dB (10 11 · I 0 ). Rock band 110 dB (10 11 · I 0 ).

Typical Problem A subway train has loudness 90 dB. A subway train has loudness 90 dB. Rock band loudness of 110 dB. Rock band loudness of 110 dB. How many times greater is the sound intensity of the band than that of the train? How many times greater is the sound intensity of the band than that of the train? The rock band is 20 dB louder The rock band is 20 dB louder Divide dB by 10 Divide dB by 10 20/10 = 2 20/10 = 2 Intensity is 10 2 or 100 times greater. Intensity is 10 2 or 100 times greater.

Harmful Impact of Sound Sounds of less than 75 decibels, even after long exposure, are unlikely to cause hearing loss. Sounds of less than 75 decibels, even after long exposure, are unlikely to cause hearing loss. Exposure to harmful sounds causes damage to the sensitive hair cells of the cochlea – the inner ear. Exposure to harmful sounds causes damage to the sensitive hair cells of the cochlea – the inner ear. Hearing injured by noise Hearing injured by noise From an intense brief impulse, such as an explosion. From an intense brief impulse, such as an explosion. From continuous exposure to noise, such as in a woodworking shop. From continuous exposure to noise, such as in a woodworking shop.

More on Hearing Loss The decibel level and time of exposure are the most important considerations. The decibel level and time of exposure are the most important considerations. Some sounds – artillery, explosions – are so loud (+140 db), ANY brief exposure to them at close range can cause permanent damage and hearing loss. Some sounds – artillery, explosions – are so loud (+140 db), ANY brief exposure to them at close range can cause permanent damage and hearing loss.

More on Hearing Loss Sounds at 100 decibels (such as loud music through stereo headphones) will take a while longer (1-2 hours of exposure) to cause permanent damage. Sounds at 100 decibels (such as loud music through stereo headphones) will take a while longer (1-2 hours of exposure) to cause permanent damage. Ipods are tested by Apple up to 103 db. Ipods are tested by Apple up to 103 db.

Standing Waves Mode of vibration in a string or column of air with unique pattern. Traveling wave that reflects off an end in such a way that the medium appears to vibrate in segments or regions. Standing wave animation. Standing wave animation

Fundamental Frequency The frequency when this pattern appears is the fundamental frequency, or “first harmonic.” This is the primary frequency you hear when you pluck a guitar string. λ/2

Second Harmonic Double the frequency and the “second harmonic” appears. λ/4

Higher Harmonics Many oscillators, including the human voice or a bowed violin string are composed of harmonics. The quality, or timbre of that sound is a result of the relative strengths of the individual harmonic frequencies.

Resonance All oscillators have a natural frequency. All oscillators have a natural frequency. Add energy in synch with that natural frequency results in resonance. Add energy in synch with that natural frequency results in resonance. Example: A swing. Example: A swing. Resonance Resonance Resonance Tacoma Narrows Bridge, WA (1940) Tacoma Narrows Bridge, WA (1940) Tacoma Narrows Bridge, WA (1940) Tacoma Narrows Bridge, WA (1940)

Doppler Frequency Shift Source moves towards you, waves are bunched up, you hear higher pitch. Source moves towards you, waves are bunched up, you hear higher pitch. Source moves away from you, waves are stretched out, you hear lower pitch. Source moves away from you, waves are stretched out, you hear lower pitch. Fire engine Fire engine Fire engine Fire engine Train Train Train Higher pitch here Lower pitch here

Beat Frequencies If two sound waves arrive at our ears simultaneously. If two sound waves arrive at our ears simultaneously. Our ears hear the average frequency of the two waves. Our ears hear the average frequency of the two waves. Also hear the intensity increase and decrease – wavering beats. Also hear the intensity increase and decrease – wavering beats. f beat = f 1 – f 2 Musicians use beat phenomena to tune their instruments. Standard for musical pitch A = 440 Hz. Musicians use beat phenomena to tune their instruments. Standard for musical pitch A = 440 Hz.

Speed of Sound v sound = 344 m/s or 1,126 ft/s (770 mi/h) at sea level and 20 °C. v sound = 344 m/s or 1,126 ft/s (770 mi/h) at sea level and 20 °C. Time for sound to go 1.0 mile = 4.7 s. Time for sound to go 1.0 mile = 4.7 s. How far is a thunderstorm? Count out seconds between lightning and thunder. How far is a thunderstorm? Count out seconds between lightning and thunder. One mile approximately every 5 seconds. One mile approximately every 5 seconds. v sound varies with temperature: if air warmer, sound goes faster. v sound varies with temperature: if air warmer, sound goes faster.

Boat moving in water faster than waves can propagate. Boat moving in water faster than waves can propagate. Forms a V−shaped wake, sometimes even from the stern of the boat. Forms a V−shaped wake, sometimes even from the stern of the boat. Move Faster Than the Wave Pressure wave build-up.

Sound Barrier Wikipedia Pressure wave build-up High−performance aircraft speeds measured in Mach numbers. High−performance aircraft speeds measured in Mach numbers. Mach 1.0 = speed of sound. Mach 1.0 = speed of sound.

Bell X-1 Chuck Yeager breaks sound barrier, Oct 14, 1947. Mojave Desert. Mach 1.06.

Supersonic Concorde supersonic transport (SST). Concorde supersonic transport (SST). Mach 2.04 (1,350 mph) cruising speed. Mach 2.04 (1,350 mph) cruising speed. You can't hear the sonic "boom" if you are inside. Why? You can't hear the sonic "boom" if you are inside. Why? First flown 1969. First flown 1969. Crash in Paris July 25, 2000. Crash in Paris July 25, 2000. Last flight October 2003. Last flight October 2003. Design characteristics inside. Design characteristics inside. Design characteristics inside. Design characteristics inside. What it felt like inside. What it felt like inside. What it felt like inside. What it felt like inside. Concord take off Concord take off Concord take off Concord take off Sonic Boom Sonic Boom Sonic Boom Sonic Boom

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