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Vibrations and Waves
Vibrations and Waves
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Vibrations and Waves
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AMPLITUDE
WAVELENGTH
CREST
TROUGH
Vibrations and Waves
Vocabulary
Transverse wave
Longitudinal wave
Reflection
Standing wave
Frequency
Vibrations and Waves
Quiz
1)How is the motion of the slinky different for transverse and longitudinal waves?
2)How does the amplitude of a single pulse change with time?
3)How does increasing the slinky’s tension affect the speed of a pulse or wave?
Vibrations and Waves
Vibrations produce waves
Vibrations of a slinky produce
Vibrations of air produce
Vibrations of electrons produce
Vibrations and Waves
Vibrations produce waves
Vibrations of a slinky produce mechanical slinky waves
Vibrations of air produce
Vibrations of electrons produce
Vibrations and Waves
Vibrations produce waves
Vibrations of a slinky produce mechanical slinky waves
Vibrations of air produce sound waves
Vibrations of electrons produce
Vibrations and Waves
Vibrations produce waves
Vibrations of a slinky produce mechanical slinky waves
Vibrations of air produce sound waves
Vibrations of electrons produce electromagnetic waves
Vibrations and Waves
Vibrations range from simple to complex.
Simple harmonic motion (SHM) is the most fundamental type of vibrational motion.
Vibrations and Waves
Vibrations range from simple to complex.
Simple harmonic motion (SHM) is the most fundamental type of vibrational motion.
Simple harmonic motion arises whenever an object moves under the influence of a restoring force proportional to its displacement.
Examples:
Vibrations and Waves
Vibrations range from simple to complex.
Simple harmonic motion (SHM) is the most fundamental type of vibrational motion.
Simple harmonic motion arises whenever an object moves under the influence of a restoring force proportional to its displacement.
Examples: Angular motion of a pendulumLinear motion of a mass on a spring
Vibrations and Waves
The mass on a spring system obeys Hooke’s Law:
F = -kx
F – restoring force of the spring [N]
k – spring constant [N/m]
x – displacement from equilibrium [m]
Vibrations and Waves
The frequency of a vibration is the number of oscillations per second.
Frequency f is measured in hertz [Hz] or “cycles per second”
Frequency is measured by counting the number of oscillations that occur in some amount of time:
Frequency = number of oscillations / time
Vibrations and Waves
Transverse wave
example: electromagnetic radiation, or a “light wave”)
Longitudinal wave
example: sound wave
Vibrations and Waves
Waves have a frequency, which is measured in hertz [Hz] or “cycles per second”
Vibrations and Waves
What is the speed of a wave?
Standing Waves on a String:The resonant modes of vibration for a string of length L
Vocabulary:
node – any point along the string that doesn’t move
antinode – points along the string where displacement is maximum
fundamental frequency – the lowest resonant frequency of the string
n = 1
n = 2
n = 3
n = 4
LVibrations and Waves
Vibrations and Waves
Do Now
If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?
Vibrations and Waves
Do Now
If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?
f1 = 440 Hz
f2 = 2 × 440 Hz = 880 HZ
f3 = 3 × 440 Hz = 1320 Hz
f4 = 4 × 440 Hz = 1760 Hz
Beets – Common name of Beta vulgaris, a plant with a swollen root which is eaten or used to make sugar
Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere
5 Hz
Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere
5 Hz
6 Hz
Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere
5 Hz
6 Hz
0.0
1.0
2.0
3.0
4.0
time [s]
Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere
5 Hz
6 Hz
0.0
1.0
2.0
3.0
4.0
time [s]
composite
Beats – periodic variations in volume heard when two sound waves with slightly different frequencies interfere
5 Hz
6 Hz
0.0
1.0
2.0
3.0
4.0
time [s]
composite
Beat frequency = absolute value of the difference between the two wave frequencies
Vibrations and Waves
Do Now
A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.
Vibrations and Waves
Do Now
A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.
a)Calculate the beat frequency
b)What are the possible frequencies being produced by the guitar string?
Vibrations and Waves
Do Now
A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.
a)Calculate the beat frequency
20 beats / 5 seconds
b)What are the possible frequencies being produced by the guitar string?
Vibrations and Waves
Do Now
A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.
a)Calculate the beat frequency
20 beats / 5 seconds = 4 beats per second
b)What are the possible frequencies being produced by the guitar string?
Vibrations and Waves
Do Now
A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.
a)Calculate the beat frequency
20 beats / 5 seconds = 4 beats per second, or 4 Hz
b)What are the possible frequencies being produced by the guitar string?
Vibrations and Waves
Do Now
A tuning fork produces a 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, 20 beats are counted in 5 seconds.
a)Calculate the beat frequency
20 beats / 5 seconds = 4 beats per second, or 4 Hz
b)What are the possible frequencies being produced by the guitar string?
396 Hz and 404 Hz
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