# WAVES.

## Presentation on theme: "WAVES."— Presentation transcript:

WAVES

What is a wave? A wave is a disturbance that passes through a medium. A wave transmits energy not matter!

What is Sound? sound is a type of wave waves are caused by vibrations. vibrations are the source of all sound. a vibration is a repeated motion.

Classifying Waves Electromagnetic Wave: is a wave which is capable of transmitting its energy through a vacuum (i.e., empty space). Electromagnetic waves are produced by the vibration of electrons within atoms on the Sun's surface. These waves subsequently travel through the vacuum of outer space, subsequently reaching Earth. Mechanical Wave: is a wave which is not capable of transmitting its energy through a vacuum. Mechanical waves require a medium in order to transport their energy from one location to another. A sound wave is an example of a mechanical wave.

Transverse Wave Transverse Waves – are due to vibrations in which particles of the medium move in a direction perpendicular to the direction motion. ex. whip.

Longitudinal Waves Longitudinal Waves – are due to vibrations in which particles of the medium move in a direction parallel to the direction of motion.

Properties of Transverse Waves
Crest: the highest point on a wave. Trough: the lowest point on a wave. Amplitude (A): the distance from the rest position to the maximum displacement. Wavelength (): the distance that one complete cycle of a wave takes.

Properties of Longitudinal Waves
Compressions: regions where the particles come together Rarefactions: regions where the particles are further apart. Wavelength (): is the midpoint between successive compressions and rarefactions.

Wave Terms cycle: one complete repetition of the pattern or vibration.
period (T): the time required to complete one cycle. Frequency ( f ): # of cycles per second. units: Hertz (Hz) How does f relate to T?

Phase Waves in phase have crests and troughs arriving at the same place at the same time. Waves out of phase have crests that arrive coincident with a trough of the second wave. Objects are out of phase if during any part of their cycles, the two objects are moving in opposite directions.

Practice Problems PG 239 #1,2 PG 240 #3,4,5

Diffraction of Waves When a straight wave propagates forward and passes through an opening the wave tends to bend or diffract. Can also occur when a wave passes an edge or around an object. Diffraction helps us explain why we can hear around corners. We tend to hear the lower bass notes more than the higher treble notes when listening to music in another room due to the fact that longer wavelengths diffract better than shorter wavelengths.

Refraction of Waves A wave can change it’s speed when it enters a new medium. It’s frequency will remain the same. i.e. if there are 10 crests approaching the boundary between the media then 10 crests should enter the new medium. The wavelength does change though. If the wave slows down the waves bunch up causing a shorter λ.

Transmission and Reflection of Waves
One dimensional waves react in a special way when they are reflected. In the case of a fixed-end reflection a crest reflects as a trough and a trough reflects as a crest. On the other hand if the reflection occurs from a free-end, where the medium or particles are free to move, there is no inversion. Crests reflect as crests and troughs reflect as troughs.

In both fixed and free end reflections there is no change in wavelength, frequency or the speed of the pulse, since the medium is the same. When a waves travels through a different medium it’s speed and wavelength change. At the boundary between the 2 media, some reflection occurs. It is called partial reflection. The phase of transmitted waves is unaffected in all partial reflections, but inversion of the reflected wave occurs when the wave passes from a fast medium to a slow medium.

Speed of Waves The Universal Wave Equation
When we create a transverse wave with a rope we must perform one complete vibration to have one complete wave. The wave travels one complete wavelength (λ) in the time it takes to complete one period of vibration (T).

We already know. If we substitute λ for ∆d and T for ∆t we get . We can also express in terms of frequency as well:

Practice PG 248. #1,2 PG 250. #1,2,3,4 PG 251. #5,6,7

(At normal atmospheric pressures)
Speed of Sound At normal atmospheric pressure and at 0° C, it is 331 m/s (about 1200km/h). If the atmospheric pressure remains constant, the speed of sound increases as the temperature increases. The speed changes by 0.6m/s for each degree Celsius. (At normal atmospheric pressures) Facts: sound travels 15 times faster in steel than it does in air sound travels 4 times faster in water than air (pg 278 for more)

Practice PG 277. #1,2 PG 279. #1,2,3 PG 280. #1,2,5,6

Mach Number We use Mach number rather than kilometres per hour for high speed aircraft like a Concorde jet. It is the ratio of the speed of the object to the speed of sound. Therefore to travel Mach 1 you must travel the speed of sound 1200km/hr. Top 50 Fastest Aircraft

The Sound Barrier Subsonic Speeds: slower than the speed of sound.
Air molecules are pushed forward by the leading edge of the wing. Compressions travel forward, faster than the wing. As a result, compressions push other air molecules out of the way. Sonic or Supersonic Speeds: at the speed of sound or greater. The compressions cannot move faster than the wing. Air molecules pile up at the front of the wing. Sometime a pile of air molecules would spill above or below the wing causing instability which resulted in many crashes.

The Sound Barrier

The Sonic Boom. This spillage of air molecules about the wing causes a shock wave to be produced. This shock wave continuously spreads out from its source. When you hear this boom it does not mean the sound barrier has just been broken rather an object in the area is flying at or faster than the speed of sound. Other examples include: flapping of a flag, crack of a whip or a wet towel.

Doppler Effect Sound from a point source:
Sound from a moving point source: Audio of a car horn.

Once the moving source reaches the speed of sound, the wave fronts pile up on one another in the direction of motion. For any moving object the waves in the direction of motion will have a smaller wavelength and higher frequency. The trailing waves have a larger wavelength and a lower frequency. Austrian mathematician and physicist, Christian Doppler ( ) 1st noticed this effect hence the name, “The Doppler Effect”

Interference when two or more waves act simultaneously on the same particles in a medium. Principle of Superposition: The resultant displacement of a given particle is equal to the sum of the displacements that would have been produced by each individual wave acting independently.

Constructive Interference
Constructive Interference: when the resultant displacement is greater than the displacement that would be caused by either wave by itself. A crest that meets a crest produces a supercrest. A trough that interferes with a trough produces a supertrough

Destructive Interference
Destructive Interference: when the resultant displacement is smaller than the displacement that would be caused by one wave itself. Web When positive and negative pulses of equal amplitude and shape, traveling in opposite directions, interfere, there is a point that remains at rest throughout the interference. This we call a node or nodal point (N). 2 Speakers

Special Interference Patterns
Standing Waves 2 Point Source Beat Frequency

*Standing Waves In stationary, or standing waves, the shape, or profile of the wave stays fixed in a medium. Ex. plucking the string of a string instrument. When the string is plucked, a wave is caused to travel up and down it. Since both ends of the string are fixed, the waveform is reflected back up and down the string, or its path, causing a wave to stay constant within it. A sound is produced because the energy within the string that is used to create the standing wave is also creating a progressive wave, the sound wave you hear.

Beat Frequency Alternating constructive and destructive interference of sound waves can be heard as a change in sound pattern from loud to soft to loud, etc. These periodic changes in sound intensity are called beats. The maximum number of intensity points that occur per second is called the beat frequency. Beat Frequency = | f1 – f2 | (where f1 & f2 are the 2 sources) Web1, Web2

When two sources have the same frequency that is f1 = f2 then no beats are heard and we can say they are in tune. As the beat frequency decreases when we adjust a source, as we would when tuning a guitar, the frequencies of each source get closer.

Practice PG 282. #1,2 PG 284. #4,5

*Standing Waves When we attach on end of a string to a stationary object and send a wave down the string the wave will return. If the returning wave is identical to the original wave a standing wave will be produced. each vibrating section is called a loop. loops alternate from being a supercrest to a supertrough it cannot be both at the same time and therefore represents half a wavelength

Frequency and Wavelength
We know that 1 loop represents half a wavelength. Therefore: λ1= 2L (L being the length of the string containing 1 loop) In terms of the universal wave equation: When 2 loops form in a string then λ2 = L. In wave equation terms:

This would mean that the second harmonic has twice the frequency as the first harmonic. Also, the third harmonic has 3 x’s the frequency as the first. Standing wave patterns are called harmonics only if their frequencies are whole-number multiples of the first harmonic.

What is Pitch? Pitch is a term that is often substituted for frequency in musical references.

Standing wave patterns in a string.
Number of Loops Scientific Name Musical Name 1 first harmonic fundamental 2 second harmonic first overtone 3 third harmonic second overtone 4 fourth harmonic third overtone

Sound quality of a musical note depends on the number and relative intensity of the overtones it produces, along with the fundamental. The pitch of a note being played on, say, a guitar depends on: The length of the string. The tension of the string. The material the string is made of.

Resonance The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object. Ex. Pushing a friend on a swing. When the frequency of forced vibrations on an object matches the object's natural frequency, a dramatic increase in amplitude occurs. This phenomenon is called resonance . Ex. The rattling dash in a car. Radio waves & antenna. 2 Tuning forks demo

When the resonance involves mechanical systems like pendulums or springs, it is known as mechanical resonance. Resonance can be destructive. Tacoma Narrows, Washington State (1940). A 64km/h wind matched the natural frequency of a suspension bridge. As time passed the bridge began to resonate and within and hour was torn apart in the middle. A similar event happened to a pedestrian bridge in London, England (2000)

Acoustical Resonance When a resonance involves sound waves we call it acoustical resonance. Ex. Blowing over the mouth of an empty bottle. Resonance can occur tube-like structures if a standing wave is setup involving air molecules.

Closed Air Columns A close end air column will produce a fixed end reflection and a standing wave will result. The bottom of the column will always be a nodal point. If the length is such that the column ends in the middle of a loop, the sound will be amplified.

Open Air Columns An open column will produce a free end reflection causing a standing wave to be produced. The end of the column will always be a antinode and the sound will be amplified.

Practice PG 302. #1,2 PG 303. #1,2 PG 305. #1,2 PG 306. #1,2,3,4,5