# Waves.

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

Waves

Waves A propagation of energy through a medium without a transfer of the medium.

Two Types of Waves 1) Transverse Wave – a wave where the disturbance of the medium is perpendicular to the direction of energy motion. Transverse Wave Diagram Transverse Diagram 1 Transverse Water Wave Transverse Wave Animation Transverse Wave Animation 1 Longitudinal Wave (Compression Wave) – a wave where the disturbance of the medium is parallel to the direction of energy motion. Sound is a longitudinal wave. Longitudinal Wave 1 Longitudinal Wave 2 Longitudinal Wave 3 Longitudinal Wave Animation Compression – a region of high density in a longitudinal wave Rarefaction – a region of low density in a longitudinal wave The amplitude is represented by the amount of compression (density). Surface Wave – A combination of transverse and longitudinal waves. Surface Wave

Components of a Transverse Wave
wavelength (λ) crest amplitude Equilibrium Position trough Crest: the location of maximum displacement on a wave. Trough: the location of the lowest displacement on a wave. Equilibrium position: the undisturbed position of the medium Amplitude: the displacement from the equilibrium position to crest or trough. The amplitude represents the energy in a wave. Wavelength (λ): the distance between the same two locations on adjacent waves.

Wave Pulse Periodic Wave A single disturbance in the medium
Wave Pulse Animation Wave Pulse Periodic Wave A repetitious wave. Transverse Wave

Two categories of waves
Matter Wave (Mechanical Wave) – a wave that needs a medium to travel through Examples: Earthquake The Earthquake Shake A vibrating guitar string The surface of water Water Surface Wave Electromagnetic Wave – a wave that does not need a medium to travel through Example: Radio waves, TV waves, light, x-rays Electromagnetic Waves

Speed of a Wave v=λ / T v=fλ wavelength (λ)
T =period: the amount of time for one wave to be created. f = frequency: the number of waves created in one second. Frequency is measured in Hertz (Hz) which has the fundamental unit of s-1 (1/s) T=1/f v=d/t = λ /T v=λ / T v=fλ Example: What is the speed of the wave above if its created in 4.0 s and has a wavelength of 12.0 m? v=λ/T = 12.0 m / 4.0s = 3.0 m/s

Speed of a wave (cont.) v=fλ λ v=d/t f= #waves / time
The above waves are created in 6.0 s and has a wavelength of 9.0 m. What is the speed of the waves? f=3 waves/6.0s =.50 Hz v=fλ=(.50 Hz)(9.0m)=4.5 m/s

Wave Properties Frequency: Increased Wavelength: Decreases
In one medium: Speed: Unchanged as it travels through a medium. The wave speed is dependent only on the properties of the medium. Frequency: Increased Wavelength: Decreases Frequency: Decreased Wavelength: Increases

A graphical explanation of why wavelength is dependent on speed:
The speed of the vehicle are constant. A larger frequency of cars: A smaller frequency of cars:

Mathematical explanation of why wavelength varies with speed:
Speed remains constant in a medium. v f = λ f Large frequency, short wavelength v = λ λ Small frequency, long wavelength v = f

Wave Properties between Media
Wave Reflection Incident wave transmitted wave reflected wave Medium 2 Medium 1 Incident wave: The original wave that approaches the boundary between two media. Reflected wave: The portion of the wave redirected back into the first medium. Transmitted wave: The portion of the original wave that the transferred into the new medium. The more similar the properties between the two media the more of the wave that is transmitted.

Phase of the Reflected Wave
phase – the position of a wave. inverted wave (180º phase shift) erect wave (0º phase shift) incident wave incident wave incident wave reflected wave reflected wave Reflected wave is erect Reflected wave is inverted If the new medium is more dense than the previous medium, the reflected wave will be inverted. If the new medium is less dense than the previous medium, the reflected wave will be erect.

Wave Interference Interference- The interaction between two or more waves simultaneously occupying the same location. Principle of superposition – the algebraic sum of two or more waves. Constructive interference will occur in the following situation when the waves occupy the same position at the same time. B A The principle of superposition shows the resulting wave of both Interfering. Constructive interference A+B B A The wave continue traveling in the same direction unaffected by the wave interference.

the same position at the same time.
Destructive interference will occur in the following situation when the waves occupy the same position at the same time. A B The principle of superposition shows the resulting wave of both Interfering. Destructive interference A+B After the interference the waves continue traveling In the same direction unaffected by the interference. A B Total Destructive interference will occur when two waves with equal magnitude, but opposite directions interfere as show below. A B A+B The waves continue traveling in the same direction unaffected by the wave interference. A B

Wave Component Properties Traveling between Media
Amplitude: Decreases Wavelength: Changes Speed: Frequency: Constant End

Wave Phenomena

Standing Waves Standing wave demonstration Standing Wave Diagram
Fluctuating stationary waves formed by the interference of traveling waves of the same frequency, speed and amplitude moving in opposite directions. Standing wave demonstration Standing Wave Diagram Standing Wave Animation Standing Wave Animation 1 Standing Wave Animation 2 Standing Wave Animation 3

Wave Fronts wave front: a short hand notation of representing the
crest of a wave.

Law of Reflection The angle of incidence is equal to the angle of reflection. (θi=θr) Incident wave Barrier θi θr Normal: a perpendicular to the surface of an object. θi=angle of incidence θr=angle of reflection Reflected wave

Refraction The change in direction of a wave when traveling from one medium to another. medium 2 medium 1 wave direction in medium 2 wave direction in medium 1

Diffraction Diffraction: the bending and spreading of a wave that passes through an opening or around an obstacle. The smaller the opening compared the wavelength of the wave, the greater the diffraction. Diffraction

Sound Audible frequency range: 20 Hz to 20 kHz
The vibration of air molecules in a medium perceivable by the human ear. Pitch – how the frequencies of sound is perceived. Audible frequency range: 20 Hz to 20 kHz Infrasonic region: Frequencies less than 20 Hz Ultrasonic region: Frequencies above 20 kHz The ultrasonic region limit is 1 GHz. Sound in air is a longitudinal wave. Sound in a liquid or gas is primarily longitudinal, but contains a small fraction of a traverse wave component.

Speed of Sound The speed of sound in air at 0ºC is 331 m/s.
The speed of sound increases as temperature increases. v=(331m/s +.6Tc) for environmental temperatures. v=331m/s(1+Tc/273m/s)1/2 for higher temperatures. Mach number: A multiple of the speed of sound Example: Mach 2 at 0ºC is 662 m/s. What is the speed of a jet traveling at Mach 3 at 0º? 993 m/s

The Doppler Effect The perceived frequency change of sound because of a wavelength change due to relative motion between a source and an observer. numerator: + source moving towards observer - source moving away from observer denominator: - observer moving towards source + observer moving away from source v = speed of sound at a given temperature vo = speed of the observer of the sound vs = speed of the source of the sound

Resonance A matched frequency between a source and an object which causes increased oscillation vibrations of the object.

Beats Fluctuations in intensity between two sound frequencies due constructive and destructive interference of the sound waves. fb=|f1-f2| fb:beat frequency