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

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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