Vibrations and Waves
Physics – 5th 6wks
Waves & Vibration: Introduction
• Vibration – a repeated back-and-forth motion, around a
fixed position. (a wiggle in time)
• Wave – a rhythmic disturbance that transfers energy
through matter or space.
• A wave is the physical effect of the movement of energy.
• A wave exists only as long as it has energy to carry.
• The source of all waves is something that vibrates (or
wiggles if you will)
Mythbusters - Metal Fusion Shockwave – YouTube
Russian Meteorite Blast Wave Impact
Nuclear Blast Wave from 1950s era
High Speed of Massive Gunpowder Explosion
Period, Cycle, and Simple
Harmonic Motion
Simple harmonic
(or periodic)
motion
• Each complete vibration is known as a cycle.
• Period – the time required to complete one cycle.
• A reoccurring, back and forth motion (like that of a
swinging pendulum) is called simple harmonic
motion.
Transverse Waves
• Transverse Waves – waves in which the motion of the medium
(what the wave is traveling through) is at right angles to the
direction that the wave is moving.
• Waves on the surface of liquids, stretched musical strings, and
the different forms of light are transverse waves.
• A pendulum that is undergoing simple harmonic motion, would
trace out a transverse wave in its movement.
Parts of a Transverse Wave
Point of equilibrium or
the midpoint
• The high points on a wave (the peaks) are known as crests.
• The low points on a wave are called troughs.
• The midpoint of the vibration, often represented by a dashed
line, is called the point of equilibrium.
Parts of a Transverse Wave
Point of equilibrium or
the midpoint
• Amplitude is the distance from the midpoint, or point of equilibrium and
either the crest or trough of the wave.
• The amplitude then equals the maximum displacement from
equilibrium.
• The greater energy that a wave has, the greater its amplitude is.
• The wavelength of a wave is the distance from the top of one crest to
the top of the next one.
• The wavelength, to put simply, is the distance between two identical
parts of a wave.
Longitudinal Waves
• Sometimes the particles of the medium move back and forth in the
same direction in which the wave travels.
• Longitudinal Waves – waves in which the particles move along
the direction of the wave rather than at right angles to it.
• Also known as Compressional Waves or Mechanical Waves.
• Sound Waves are longitudinal waves.
• sound waves and a Rubens Tube
• Rubens Tube and basic tones
Longitudinal Waves
• The dense, compressed area of a longitudinal wave is
called a Compression.
• The lower density region of a longitudinal wave is called a
Rarefaction.
• The wavelength is measured either between two
compressions or two rarefactions.
• The more dense the medium becomes upon compression,
the greater the longitudinal wave’s amplitude.
Parts of a Longitudinal Wave
rarefaction
wavelength
compression
Ruben’s Tube & Sound Waves
Rarefaction
Compression
A Rubens’ Tube is a metal tube sitting horizontally with tiny holes drilled in a line
along the top. One end of the Rubens’ Tube is connected to a small tank of propane like
those used when camping, and the other end of the Tube is connected to a speaker.
When a sound is played through the speaker, the wave of energy compresses the
propane gas inside of the tube and propane escapes out of the tiny holes on top. If the
gas coming out of the holes is ignited, the flames will be taller where the gas is
compressed and shorter where the gas particles are less dense.
Waves through Water
• Note waves of energy through water can behave like longitudinal
waves in the water and as transverse waves on the surface where the
water meets the air.
Earthquake/Seismic Waves
• Earthquakes move as a combination of the two – as
P waves (pressure waves – or longitudinal) and S Waves
(transverse waves). Matter tends to move in an elliptical pattern as
the waves of energy move through the ground
Frequency
• How often a vibration occurs is described by its frequency
• One back and forth motion would be a cycle.
• If this happened in one second, the frequency would be 1 cycle
per second. If two vibrations happened in 1 second, the
frequency would be 2 cycles per second, etc.
• The unit for frequency is called the Hertz (named after the
German scientist Heinrich Hertz who was the first to produce &
receive radio waves) and its symbol is Hz
• A frequency of 1 cycle per second is equal to 1 Hz and a
frequency of 2 cycles per second is equal to 2 Hz , and so on.
The relationship between Period and
Frequency
• If the frequency of a vibrating object is
known, its period can be calculated, and vice
versa.
• If something vibrates twice in 1 second, its
frequency is 2 Hz . Therefore, the time it
took for one vibration to occur was ½ second.
• If the frequency of an object was 3 Hz, then
the period or time for one vibration to occur
would be 1/3 sec .
• The period then is the reciprocal of the
frequency and the frequency is the
reciprocal of the period.
• Note: raising anything to the negative one
power is the same as finding its reciprocal
(or dividing it into 1)
Note: Frequency is in Hz
Period is in seconds
Circle diagram for the relationship between
Period & Frequency of a Wave or Vibration
1=T×𝐹
T=
1
𝐹
1
F=
𝑇
1
Units:
Period = seconds
Frequency = Hz
F
T
T = Period (of time)
F = Frequency
1
𝐹
Remember: that is the same as doing 𝐹 −1
Example Problem 1: Period from Frequency
If something vibrated 30 times every second (meaning it had a frequency
of 30 Hz) how long did it take it to vibrate once?
take the inverse of 30 Hz (or 30/sec)
1 𝑠𝑒𝑐
Period =
30
1
Period =
sec
30
Period ≈ 0.03 𝑠𝑒𝑐
Example Problem 2: Frequency from the Period
If something vibrated once every 0.25 sec, at what frequency did it
vibrate at?
take the inverse of 0.25 sec
Frequency =
that is, 4 times every second
1
0.25 𝑠𝑒𝑐
Frequency = 4 Hz
Wave Speed
• Speed, frequency, and wavelength of a wave are related.
• In the formula for wave speed, speed is v, frequency is f, and
wavelength is the Greek letter Lambda -
λ
• The units for wave speed are always a derived unit of distance divided
by time.
• If the wavelength between two crests of waves on the ocean is 3
meters, and 2 crests pass by a stationary point each second, then the
wave speed is 3 meters x 2 cycles/second = 6 meters/second.
Note: frequency will be in Hz, wave speed will be in m/s, and wavelength will be in m
Circle diagram for the Wave Speed formula
v=λ×𝑓
f=
v
λ=
𝑣
𝑓
Units:
Wave Speed = meters/second
Frequency = Hz
Wavelength = meters
λ
f
v = wave speed
λ = wavelength
f = frequency
𝑣
λ
Example Problem #3: Finding Wave
Speed
The frequency of a wave is 40 Hz, and the wavelength of the wave is
0.8m. What is the speed of the wave?
𝑣 = 40 𝐻𝑧 × 0.8 𝑚
40
𝑣 =
× 0.8 𝑚
𝑠𝑒𝑐
v = 32 m/s
Example Problem #4: Finding
wavelength
The speed of a sound wave is 343 m/s and has a frequency of 500 Hz.
What is the length of the wavelength?
𝑣
λ=
𝑓
343 𝑚/𝑠
λ=
500 𝐻𝑧
343 𝑚/𝑠
λ=
500/𝑠𝑒𝑐
λ=
343 𝑚
𝑠𝑒𝑐
λ = 0.686 m
×
𝑠𝑒𝑐
500
Example Problem #5: Finding the frequency
The wavelength of a wave is 0.002 m and it has a wave speed of
0.05 m/s. What is the frequency of that wave?
𝑣
f=
λ
0.05 𝑚/𝑠
f=
0.002 𝑚
f=
0.05 𝑚
𝑠𝑒𝑐
f = 25/second
f = 25 Hz
×
1
0.002 𝑚