Waves Waves are everywhere. Sound waves, visible light waves, radio waves, microwaves, water waves,...

WavesWaves

Waves are everywhere. Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, cosine

waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of our daily

encounters with waves.

WavesWaves

A wave can be described as a disturbance that travels through a medium from one location to another location.

The Nature of a WaveThe Nature of a Wave

Consider the slinky– When a slinky is stretched from end to end and is held

at rest, it assumes a natural position known as the equilibrium or rest position.

The Nature of a WaveThe Nature of a Wave

Consider the slinky– To introduce a wave into the slinky, the first coils are

displaced or moved from its equilibrium or rest position. The coils might be moved upwards or downwards, forwards or backwards; but once moved, it is returned to its original equilibrium or rest position.

The Nature of a WaveThe Nature of a Wave

Consider the slinky– The act of moving the first coils of the slinky in a given

direction and then returning it to its equilibrium position creates a disturbance in the slinky.

The Nature of a WaveThe Nature of a Wave

Consider the slinky– If the first coil of the slinky is given a single back-and-

forth vibration, then we call the observed motion of the disturbance through the slinky a pulse. A pulse is a single disturbance moving through a medium from one location to another location.

The Nature of a WaveThe Nature of a Wave

Consider the slinky– The repeating and periodic disturbance which moves

through a medium from one location to another is referred to as a wave.

– A medium is a substance or material which carries the wave.

– Waves are said to be an energy transport phenomenon.

Types of WavesTypes of Waves

A Transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves.

Slinky Demo

Types of WavesTypes of Waves

A Longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves.

Slinky Demo

Types of WavesTypes of Waves

A Surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse.

Video in 3 slides

Surface WaveSurface Wave

Water Waves– A wave moving across the surface of an ocean, lake,

pond or other body of water. The waves are created by some form of a disturbance, such as a rock thrown into the water or a boat moving through the water. The water wave has a crest and a trough and travels from one location to another.

Surface WaveSurface Wave

In longitudinal and transverse waves, all the particles in the entire bulk of the medium move in a parallel and a perpendicular direction (respectively) relative to the direction of energy transport. In a surface wave, it is only the particles at the surface of the medium which undergo the circular motion.

Surface WaveSurface Wave

Another view

Properties of WavesProperties of Waves

Properties of WavesProperties of Waves

A Transverse Wave– The crest of a wave is the point on the medium which exhibits

the maximum amount of positive or upwards displacement from the rest position. The trough of a wave is the point on the medium which exhibits the maximum amount of negative or downwards displacement from the rest position.

Slinky Demo

Next

Properties of WavesProperties of Waves

A Transverse Wave– The amplitude of a wave refers to the maximum

amount of displacement of a particle on the medium from its rest position on a wave.

Slinky Demo

Properties of WavesProperties of Waves

A Longitudinal Wave– A compression is a point on a medium through which a longitudinal

wave is traveling which has the maximum density. The amplitude of a longitudinal wave is a measure of how compressed the medium becomes.

Slinky Demo

Next

Properties of WavesProperties of Waves

A Longitudinal Wave– A rarefaction is a point on a medium through which a

longitudinal wave is traveling which has the minimum density.

Slinky Demo

Properties of WavesProperties of WavesWavelength

– The wavelength of a wave is simply the length of one complete wave cycle.

Properties of WavesProperties of WavesFrequency

– The frequency of a wave is the number of complete waves that pass a given point in a certain amount of time.

– Frequency is expressed in Hertz (abbreviated Hz) where 1 Hz = 1 cycle/second.

Properties of WavesProperties of Waves Speed

– The speed of a wave is how far a wave travels in one unit of time, or the distance divided by the time.

– Speed = Wavelength * Frequency

– Or…Frequency = Speed / Wavelength

Interaction of WavesInteraction of Waves

Interaction of WavesInteraction of WavesReflection

– When a wave hits a surface through which it cannot pass, it bounces back

Interaction of WavesInteraction of WavesAngle of Incidence

– The angle of incidence is the angle between the incoming wave and an imaginary perpendicular line to the surface.

Interaction of WavesInteraction of WavesAngle of Incidence.

The angle of reflection is the angle between the reflection and the imaginary line.

Interaction of WavesInteraction of WavesRefraction

– Refraction is seen when a wave moves from one medium to another at an angle, it changes speed as it enters the second medium causing it to bend.

Aquarium Demo

Interaction of WavesInteraction of WavesDiffraction

– Diffraction is seen when a wave passes a barrier or moves through a hole in a barrier, it bends and spreads out.

Wave Tank Demo

Interaction of WavesInteraction of WavesInterference

– When two or more waves meet

Interaction of WavesInteraction of WavesConstructive Interference

– When two or more waves combine to make a wave with a larger amplitude.

Interaction of WavesInteraction of WavesDestructive Interference

– When the amplitudes of two or more waves combine to produce a wave with a smaller amplitude.

Making WavesMaking Waves

The Pan Flute– A pan flute is a group of tubes with a closed end. Each

tube have a different length but, usually, the same diameter of all other tubes.

– The length of the tube influence the pitch: longer tubes produce lower notes, shorter tubes produce higher notes.

– The inner diameter of the tube influence the speed of blow needed to make the sound audible: smaller diameter means less blow, greater diameter means more blow.

Calculating WaveLengthCalculating WaveLength

Wavelength(ƛ) is equal to the speed of sound(v) divided by the frequency(f) of the sound.– ƛ = v/f v is in m/s, f is in Hz– ƛ is in meters– v = 346.65m/s (Around room temp)

Calculating Tube LengthCalculating Tube Length

First consider the tube, open on one end, closed on the other…

Calculating Tube LengthCalculating Tube Length

The closed end would be a fixed point…like where the strings attach on a guitar. The open end would be the furthest the wave could swing.

Calculating Tube LengthCalculating Tube Length

So, if I shrink it down……You can see that what was in the tube was only about ¼ of a whole wavelenght.

Calculating Tube LengthCalculating Tube Length

Therefore….the formula for calculating tube length needs to be something like this.– L = v / 4 x f– Where L is in m, – f is in Hz– v = 346.65m/s (Around room temp)

Pentatonic ScalesPentatonic Scales

The pentatonic scale consists of five notes within one octave without any semitones or tritones. Thus no clashing dissonant intervals.

the C major pentatonic (C - D - E - G – A)

Pentatonic ScalesPentatonic Scales

Note Frequency (Hz) Wavelength (cm)

C 261.6 132

D 293.7 117

E 329.6 105

G 392.0 88.0

A 440.0 78.4