# A “wiggle” or “oscillation” or “vibration” produces a Wave

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A “wiggle” or “oscillation” or “vibration” produces a Wave
Waves A “wiggle” or “oscillation” or “vibration” produces a Wave

Types of Waves Mechanical Waves
Require a material through which to travel- a “material medium” Examples: water, rope, sound, slinky

c = 3 x 108 m/s Electromagnetic Waves
They can travel through empty space- a vacuum- they don’t require a material medium. Examples: x-rays, UV, visible light, infrared, … In a vacuum, they all travel at the same speed— The “speed of light” This speed is constant and is called “c”. c = 3 x 108 m/s

Wave Motion Transverse Waves
The wave disturbance is PERPENDICULAR to the direction of the wave’s velocity. “Crest”, the peak of the wave “Trough”, the valley of the wave “Equilibrium” line

Longitudinal Wave (compression wave) The wave disturbance is PARALLEL to the direction of the wave’s velocity.

How does this motion make a “wave”??

Sound is a longitudinal wave. *
Molecules move parallel to the direction of the waves velocity. Areas of high pressure and low pressure “compression” and “rarefaction”

Wave pulse- one disturbance

Polarized waves If there are many waves and ALL the waves are vibrating in the same plane, they are said to be “polarized”

Measurements Wavelength, l
Distance between points where the wave pattern repeats- Measured in meters

Amplitude, A Maximum distance above or below equilibrium- Measured in meters As the amplitude increases, the energy the wave transmits also increases.

f = 1 / T and T = 1 / f f = 6 waves / 12 s = 0.5 Hz T = 1 / f = 2 s
Period, T Shortest time interval during which the pattern repeats--- measured in seconds Frequency, f The number of waves per second-- Measured in Hz f = 1 / T and T = 1 / f Example: While watching waves go by a pier, you count 6 waves every 12 seconds. What is the frequency and period of the waves? f = 6 waves / 12 s = 0.5 Hz T = 1 / f = 2 s

Velocity, v The velocity of a wave depends on what kind of material through which it is traveling. For example, ALL sound waves, regardless of their pitch, travel at the same speed through air and at the same speed through water. But the speed in water is faster than the speed in air!

The velocity of a wave depends on the medium through which is travels
The velocity of a wave depends on the medium through which is travels. If you know some things about the medium, you can find the velocity by “Modulus”- a characteristic of different substances Bulk modulus- fluids Elastic modulus- solids

Velocity, v You can find that speed if you know both the wave’s period and its wavelength: Velocity = Distance / time = l/T, so v = l/T but since frequency, f = 1/T, v = lf

Water Wave “Surface” water waves are combinations of transverse and longitudinal waves.

Waves transmit energy without transmitting matter.
Most waves move through a substance but only move it backwards and forwards (longitudinal) or up and down (transverse) while the wave passes. After the wave has gone, the substance is back where it started but energy has been carried by the wave from its origin (where it begins) to its destination (where it finishes).

Get a calculator!!!

Period = time per wave Frequency = waves per time If you observe 3 waves go by every 9 seconds, what is the period of the wave? The frequency? T = 3 s f = 1/3 Hz

A sound wave moves at about 343 m/s through air
A sound wave moves at about 343 m/s through air. The musical note “C” has a frequency of 128 Hz. What is its wavelength in air? v = lf l= v/f = 343 m/s / 128 Hz l = 2.7 m

What is the frequency of red light, whose wavelength is 620 nm
What is the frequency of red light, whose wavelength is 620 nm? nm = 10-9 m Velocity = c = 3 x 108 m/s v = lf f = c / l f = 3E8 / 620E-9 f = 4.8E14 Hz

Two different sound waves are produced by different band instruments- 512 Hz and 106 Hz. Which has a longer wavelength? Since the velocity is the same for both, the smaller frequency has the larger wavelength! v = lf

Behavior of Waves

Behavior of All Waves Reflect: To bounce back from a surface
Law of Reflection: The angle of reflection is equal to the angle of incidence.

Refraction: The change in direction as a wave passes from one medium into another.
Particles ALSO refract when they enter a new medium!

Diffraction: The curving of a wave around boundaries or barriers or through small openings.
This behavior is unique to waves. Particles do NOT diffract (spread out, curve)

Simulations More simulations

What happens to a wave when….
…the medium through which it travels changes? If the medium changes, the velocity changes! (as well as the wavelength) … and the wave REFRACTS!

What happens to a wave when….
…it runs into another wave? The two waves will pass right through each other During the time of intersection, the size of the resulting wave is determined by SUPERPOSITION- Adding the displacements from equilibrium together.

Constructive Interference:
Waves are on same side of equilibrium

Destructive Interference: waves are on opposite side of equilibrium

“in Phase”

“out of Phase” The peaks and troughs do NOT line up with each other

What happens when…. … a wave reflects back upon itself?
It MAY result in a standing wave. Node: the locations along a standing wave where the medium is undisturbed. Antinode: the locations where there is maximum displacement.

Sound

Sound is a longitudinal, mechanical wave. *
Molecules move parallel to the direction of the waves velocity. Areas of high pressure and low pressure “compression” and “rarefaction”- molecules are compressed and than move apart

Requires a vibrating object
Guitar string Stereo speaker Voice: vocal cords *

Speed of sound As sound travels through air, at 20˚C (68˚F) and sea level pressure, v is about 343 m/s v = lf As the temp goes up, the velocity increases- Why?? As the density of the medium goes up, the velocity increases- Why?? Travels much slower than light Count time from when you see the flash of lightning to when you hear the thunder- divide by 5 = miles to lightning

The velocity of a wave depends on the medium through which is travels
The velocity of a wave depends on the medium through which is travels. If you know the medium, you can find the velocity by Bulk modulus- fluids Elastic modulus- solids

Sound Wave Behavior Reflect: an echo Refract: changes direction when the medium changes Diffract: curves around barriers and through openings

You stand at the edge of a canyon and yell, “Hello. ”
You stand at the edge of a canyon and yell, “Hello!”. If you hear the echo 3 seconds later, how wide was the canyon? vsound = 343 m/s d = vt The time for the sound wave to strike the opposite canyon wall is ½ the total time. d = (343 m/s) (1.5 s) d = m

If you drop a rock at the top of a 40 meter high cliff, how long will it be until you hear the sound when it hits the ground? Total time = time for the rock to fall + time for the sound to travel back to you. d = vot + ½ at2 Time for the rock to fall: vo = 0, a = g d = ½ at2 Time for the sound: a = 0, v = 343 m/s d = vt

What kind of sound wave is produced when the source of the sound is moving?

A “shock wave” is produced from these overlapping waves
A “shock wave” is produced from these overlapping waves. It produces a loud “sonic boom”. Sonic booms occur when the source of sound exceeds the speed of sound * Sonic Booms captured on video

Reflection Echo Sonar: invented in a reflected sound wave is used underwater instead of light because light is more easily absorbed by water, so sound will travel much farther. Ultrasound Autofocus cameras

Pitch Determined by the frequency Hi frequency = high pitch
Musical notes- if you double the frequency you go up by one OCTAVE Example: 400 Hz, 200 Hz, 800 Hz Range of hearing humans 20 Hz up to about 20,000 Hz dogs up to about 50,000 Hz cats up to about 70,000 Hz

The Doppler Shift A detected change in the frequency of a wave as the source of the wave moves Police siren, car horn, weather, stars

Wave Amplitude For a sound wave, the wave amplitude corresponds to the VOLUME. Loudness is measured in decibels, dB Where zero decibels is the threshold of human hearing and 120 dB is the point at which sound becomes painful and hearing can be damaged.

Resonance- the tendency of an object to vibrate with a greater amplitude at certain frequencies
One simple example is pushing a child on a swing. If two objects are vibrating with the same frequency, they are said to be “in resonance” Examples: two tuning forks- if they are “in resonance”, the vibration of one will produce vibration in the other even if they are not touching.

Beats A “beat frequency” is produced when two objects are vibrating at nearly the same frequency. Used for tuning orchestral instruments Beat frequency = f1 – f2

Resonance All rigid objects have a “natural” frequency or group of frequencies at which they will vibrate with greater amplitude. These frequencies are based on many factors like mass, density, shape, elasticity, etc. When exposed to an external source of their natural resonate frequency, they will begin to vibrate in response.

Resonance Even very large objects can have a resonant frequency at which they will vibrate in all different modes. Broughton Suspension Bridge was a suspended-deck suspension bridge built in 1826 to span the River Irwell between Broughton and Pendleton, now in Greater Manchester, England. It was one of the first suspension bridges constructed in Europe. On 12 April 1831 the bridge collapsed, reportedly owing to a mechanical resonance induced by troops marching over the bridge in step.[1] A bolt in one of the stay-chains snapped, causing the bridge to collapse at one end, throwing about forty of the men into the river. As a result of the incident the British Military issued an order that troops should "break step" when crossing a bridge. Wikipedia Millennium bridge Tacoma Narrows bridge

Resonance For musical instruments, the resonant frequency of the instrument can be changed by adjusting the length of the chamber or string. The same string will vibrate at different resonant frequencies shown by “standing waves” along the string. Standing Waves along a string

Resonators All musical instruments create standing wave forms within them. Wind instruments: waves of air molecules inside the cavities Stringed instruments have vibrating strings, but the majority of sound is produced when that vibration is spread to a resonating box, often called the “sound board” or “sound box”

Standing Waves

Standing Waves in an “Open Pipe” resonator
The standing wave always has a node at each end of the pipe or string. The “fundamental frequency”- the lowest note, is produced when only ½ of a wave is being generated. Length of pipe = ½ of a wavelength

Harmonics Other frequencies, called “harmonics” are produced AT THE SAME TIME as the fundamental frequency. 2nd Harmonic Length = one wavelength The frequency (pitch) is higher, the wavelength is smaller.

3rd Harmonic Length = 1 ½ wavelengths

Transverse waves along a string- example: a guitar string
Resonance (Open Pipe)

3rd Harmonic Example: If the standing wave above has a frequency of 4 Hz in an open pipe of length 1.2 m, what is the velocity of the wave? v = lf What is the wavelength l, if the length of the pipe is 1.2 m? There are 1 ½ wavelengths in the pipe, therefore L = 1.5 l l = 0.8 m v = (0.8 m)(4 Hz) = 3.2 m/s

Closed Pipe Resonators
Node at open end. Antinode at closed end. Fundamental frequency: Length = ¼ of a wavelength

Closed Pipe Resonators
2nd Harmonic Length = ¾ of a wavelength

For the same length, which type of organ pipe will produce a lower note, an open pipe or a closed pipe? A closed pipe!