WAVE MOTION

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Wave Motion- any disturbance propagated in a medium such as string, air, etc. Types of waves: 1. Mechanical waves waves that are produced in matter such as solid, liquid and gas 2. Electromagnetic waves- waves that are produced in electric and magnetic fields and can propagate even in vacuum or empty space.5/4/12

Types of Mechanical Waves1. Transverse waves- waves which occur when the particles of the medium vibrate perpendicularly to the direction of the wave propagation.Ex. Waves produced on a vibrating string Illustration: A A N ANode, N pt. of no vibration Antinode,A- pt. of maximum vibration Direction of wave propagation

N

N

A

N

N

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2. Longitudinal waves- waves which occur when the particles of the medium vibrate parallel to the direction of wave propagation. They are also called compressional waves. Ex. Sound wave

Compression or Condensation- region where particles are near each other Rarefaction- the region where the particles are far apart from each other5/4/12

Properties of a wave: 1. Speed or Velocity (v)- the distance traveled per unit time. (cm/sec, m/sec, ft/sec) 2. Frequency (f)- the number of similar waves which pass through a point per unit time or number of vibrations made by a particle per unit time. (vps, cps, hertz or hz) 3. Wavelength ( )- the length of one complete wave between two points 5/4/12 which are in phase. (cm, m, ft)

Frequency of Vibrating String / WireL

Consider a vibrating string:wavelengt h,

vA N N A N

v

segment

segment

Velocity of Transverse Wave (for vibrating string)

W

Frequen cy, f(stri ng)

Velocity of Transverse Wave (for vibrating wire)

(wir e)

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NOTE:

n corresponds to the nth harmonic frequency mode. nth harmonic frequency mode corresponds to the nth overtone +1 Example:

A string vibrates in the harmonic n segment = 12 A string vibrates in the 5/4/12 overtone

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Mathematical Description of a WaveWave function for a sinusoidal wavewave function that describes the wave. This gives the displacement (from equilibrium) of any particle at any time Sinusoidal wave moving in (+) x direction Sinusoidal wave moving in (-) x directionals o

Where: V - wave speed (m/s, cm/s) - angular frequency (rad/sec) k wave number - wavelength

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Determining the Velocity

Particle Velocity and Acceleration in a Sinusoidal Wave

Determining the Acceleration (with respect to t)

Determining the Acceleration(with respect to x)

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5. A transverse sine wave with an amplitude of 2.50 mm and a wavelength of 1.8 m travels from left to right along a long, horizontal, stretched string with a speed of 36 m/s. Take the origin at the left of the undisturbed string. At time t= 0 the left end of the string has its maximum upward displacement. (a) What are the frequency, angular frequency and wave number of the wave? (b) What is the function y(x,t) that describes the 5/4/12

6. One string of a guitar lies along the x-axis when in equilibrium. The end of the string at x=0 (the bridge of the guitar) is tied down. An incident sinusoidal wave travels along the string in the x direction at 143 m/s with an amplitude of 0.750 mm and a frequency of 440 Hz. This wave is reflected from the fixed end at x=0, and the superposition of the incident traveling wave and the reflected traveling wave forms a standing wave. 5/4/12