introduction to waves
DESCRIPTION
Introduction to Waves. How do you describe the motion of a pulse traveling through the slinky?. Watch the video clip: Making_Pulses Sketch what you observe. Draw a picture of a pulse and label the parts including: amplitude and equilibrium (rest position). - PowerPoint PPT PresentationTRANSCRIPT
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Introduction to Waves
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How do you describe the motion of a pulse traveling through the slinky?
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How do you describe the motion of a pulse traveling through the slinky?
Watch the video clip: Making_Pulses• Sketch what you observe. Draw a picture of a
pulse and label the parts including: amplitude and equilibrium (rest position).
Equilibrium positionAmplitude
Pulse Length
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Is the speed of a pulse constant?
• Propagating_Pulses.mov
Create a position vs. time graph. Use the meterstick in the background for a distance scale. The video frame rate is 30 frames per second, so the time elapsed between frames is 1/30 s.
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Pulse Speed
The graph should be linear… so the speed is constant!
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How do you describe the motion of a particle in the spring as a pulse passes through?
Tie a string to the midpoint of a slinky. Send a pulse through the slinky and describe themovement of the string.
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How do you describe the motion of a particle in the spring as a pulse passes through?
Motion of particle in spring/slinky is perpendicular to the motion of the pulse!We call this a TRANSVERSE pulse.
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What is the difference between a pulse and a wave?
Pulse = Single event
Wave = Multiple pulses sent continuously
Pulse Wave
Wave length =
AmplitudeAmplitude
Pulse length
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How do you calculate the speed of a pulse/wave?
1. Speed = distance / time 2. Speed = wavelength * frequency = f3. Speed = T= tension of string/slinky= linear mass density or mass/length
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Fixed and Free End (Assuming no Friction)
• What happens to the amplitude of a pulse as it travels down the slinky and back?
• What happens to the speed of a pulse as it travels down the slinky and back?
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Fixed and Free End (Assuming no Friction)
• What happens to the amplitude of a pulse as it travels down the slinky and back?
Stays the same
• What happens to the speed of a pulse as it travels down the slinky and back?
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Fixed and Free End (Assuming no Friction)
• What happens to the amplitude of a pulse as it travels down the slinky and back?
Stays the same
• What happens to the speed of a pulse as it travels down the slinky and back?
Stays the same
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Fixed vs. Free EndWhat is the shape of the pulse after it comesback down the slinky after hitting the fixed end?Fixed End
What is the shape of the pulse after it comes back down the slinky after hitting the free end?
Free End
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Fixed vs. Free EndWhat is the shape of the pulse after it comesback down the slinky after hitting the fixed end?Inverted What is the shape of the pulse after it comes back down the slinky after hitting the free end?Upright
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Interacting at a Boundary–Reflection and Transmission Involving Two Media
Condition Reflection (I or U) Transmission (I, U or N)Slinky Fixed EndSlinky SnakySnakey Slinky
Snakey Free End
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Interacting at a Boundary–Reflection and Transmission Involving Two Media
Condition Reflection TransmissionSlinky Fixed End Inverted NoneSlinky SnakySnakey SlinkySnakey Free End
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Interacting at a Boundary–Reflection and Transmission Involving Two Media
Condition Reflection TransmissionSlinky Fixed End Inverted NoneSlinky Snaky Inverted UprightSnakey SlinkySnakey Free End
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Interacting at a Boundary–Reflection and Transmission Involving Two Media
Condition Reflection TransmissionSlinky Fixed End Inverted NoneSlinky Snaky Inverted UprightSnakey Slinky Upright UprightSnakey Free End
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Interacting at a Boundary–Reflection and Transmission Involving Two Media
Condition Reflection TransmissionSlinky Fixed End Inverted NoneSlinky Snaky Inverted UprightSnakey Slinky Upright UprightSnakey Free End Upright None
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Superposition- What happens when waves or pulses interact?
1. Two pulses from opposite sides: opposite superposition
2. Two pulses from same side: same superposition
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Superposition- What happens when waves or pulses interact?
1. Two pulses from opposite sides:
2. Two pulses from same side: same superposition
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Superposition- What happens when waves or pulses interact?
1. Two pulses from opposite sides:
2. Two pulses from same side:
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Standing Waves
When we send pulses down string or slinky at certain frequencies we produce standing waves… let’s see an example. Standing Wave Movie
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Do you see a pattern for calculating frequency for each standing wave?
Length of String (m)
Speed (m/s)
Sketches (m) Frequency =?
f = v/
5 6.0 2* L or 10 m f = v/2L
0.6 Hz5 6.0 1L or 5m f = v/L
1.2 Hz5 6.0 2/3 L or
3.33m f = 3v/2L
1.8 Hz5 6.0 ½ L or 2.5 m f = 2 v/L
2.4 Hz5 6.0 2/5 L or 2 m f = 5v/2L
3 Hz
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Two Fixed End Standing Waves
Frequency for a standing wave produced with two fixed ends with n antinodes.
n = 1, 2, 3…
NodeAntinode
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What if only one end was fixed…
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Do you see a pattern for calculating frequency for each standing wave?
Length of String (m)
Sketches (m) Frequency =?
f = v/
L 4L f = v/4L
L 4/3 L f = 3v/4L
L 4/5 L f = 5v/4L
L 4/7 f = 7 v/4L
L 4/9 f = 9v/4L
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One Fixed End Standing Waves
Frequency for a standing wave produced with one fixed end
n = 1, 3, 5…
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Sound!
Two major differencesLongitudinal WaveSpeed
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Speed of SoundSpeed =
B = bulk modulus is the mathematical description of an object or substance's tendency to be deformed elastically
= density
Sound is faster in a more elastic and less densemedium.
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Sound is a Longitudinal Wave
Particle motion is parallel to motion of wave or pulse.
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SuperpositionAmplitude = Loudness… Constructive Interference = LOUD Destructive Interference= no sound
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Interference of Sound WavesConstructive Interference: Path Difference is zero or some integer multiple of wavelengths
d = 0, 1, 2, 3,….
Destructive Interference: Path Difference is ½ , 1 ½ , 2 ½ , etc wavelengths
d = ½ , 3/2 , 5/2 ,….
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Path length difference is 0. Two wave crests will meet creating constructive . LOUD
Path length difference is 1/2 . Wave crest and trough will meet creating destructive interference…. No sound.
2 2
2 3/2
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Interference ExampleTwo speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance 0.350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound)
3.0 mO8.0 m
P
0.350 m
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Interference ExampleTwo speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance 0.350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound)
3.0 mO
8.0 m
P
0.350 m
Path length for speaker 2 = 8.08 m
Path length for speaker 1 =8.211
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Interference ExampleTwo speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance 0.350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound)
3.0 mO
8.0 m
P
0.350 m
Path length for speaker 2 = 8.08 m
Path length for speaker 1 =8.21 Path length difference = 0.13 m
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Interference ExampleTwo speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, which is located 8.00 m from the center of the line connecting the two speaker. The listener then walks to point P, which is perpendicular to the distance 0.350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take the speed of sound in air to be 343 m/s. (Minimum = no sound)
Path length difference = 0.13 m
First minimum occurs when the difference is /2 so….
0.13 m = /2 = 0.26 m
= 0.26 mV = 343 m/s
So f = 1.3 kHz
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Two identical loudspeakers face each other at a distance of 180 cm and are driven by a common audio oscillator at 680 Hz. Locate the points between the speakers along a line joining them for whichthe sound intensity is (a) maximum (b) minimum. Assume the speed of sound is 340 m/s.
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Beats
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Doppler Effect
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Doppler Effect
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Shock Waves
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Standing Waves for Sound
Can you find the pattern for the harmonic frequencies?
Sometimes called fundamental frequency.
Sometimes called first overtone.
Sometimes called second overtone.
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Standing Waves for Sound
Can you find the pattern for the harmonic frequencies?
n= 1, 2, 3…
Sometimes called fundamental frequency.
Sometimes called first overtone.
Sometimes called second overtone.
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Standing Waves for Sound (Closed End)
Can you find the pattern for the harmonic frequencies?
N = 1, 3, 5, etc
Sometimes called fundamental frequency.
Sometimes called 1st overtone.
Sometimes called 2nd overtone.
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Intensity
Intensity is average power/ area = P/4r^2