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Introduction mechanical waves electromagnetic wavesMechanical waves Waves are two main types : mechanical waves and electromagnetic waves. Mechanical waves, what we interpret as a wave corresponds to the propagation of a disturbance through a medium The mechanical waves require (1)some source of disturbance, (2) a medium that can be disturbed, (3) some physical connection through which adjacent portions of the medium can influence each other

BASIC VARIABLES OF WAVE MOTION BASIC VARIABLES OF WAVE MOTION - The wavelength λ is the minimum distance between any two identical points (such as the crests) - The Period T is the time required for two identical points (such as the crests) of adjacent waves to pass by a point. - The frequency is the number of crests (or troughs, or any other point on the wave) that pass a given point in a unit time interval.

- The amplitude A of the wave is the maximum displacement of a particle of the medium DIRECTION OF PARTICLE DISPLACEMENT Transverse wave A traveling wave that causes the particles of the disturbed medium to move perpendicular to the wave motion is called a transverse wave. longitudinal wave is a travelling wave that causes the particles of the medium to move parallel to the direction of wave motion.

ONE-DIMENSIONAL TRAVELING WAVES ONE-DIMENSIONAL TRAVELING WAVES the wave function y represents the y coordinate of any point P of the medium at any time t. Consider a point P on the string, identified by a specific value of its x coordinate. As the wave passes P, the y coordinate of this point increases, reaches a maximum, and then decreases to zero. Therefore, the wave function y represents the y coordinate of any point P of the medium at any time t.

Then, the wave function could be written as For a wave travelling to the right For a wave travelling to the left Regardless of how x and t change individually, we must require that in order to stay with the crest. This expression therefore represents the equation of motion of the crest. At t = 0, the crest is at x = x 0 Hence, the wave speed is

In destructive interference the displacements caused by the two Pulses are in opposite directions. SUPERPOSITION AND INTERFERENCE superposition principle superposition principle : If two or more travelling waves are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of the individual waves. In constructive interference the displacements caused by the two pulses are in the same direction.

THE SPEED OF WAVES ON STRINGS If the tension in the string is T and its mass per unit length is µ, then, the wave speed v is Let us verify that this expression is dimensionally correct. The dimensions of T are ML/T 2, and the dimensions of µ are M/L. Therefore, the dimensions of T/µ are L 2 /T 2 ; hence, the dimensions are L/T— which is the dimensions of speed.

SINUSOIDAL WAVES The wave represented by this curve is called a sinusoidal wave The function describing the positions of the particles of the medium through which the sinusoidal wave is travelling can be written as Where, A is the wave amplitude and λ the wavelength. The wave moves to the right with a speed v, this at some later time t.

By definition, the wave travels a distance of one wavelength λ in one period T. Therefore Substituting for v into Equation we find that We can express the wave function in a convenient form by defining two other quantities, the angular wave number k and the angular frequency ω :

Using these definitions, we see that Equation of motion can be written in the more compact form, The frequency f of a sinusoidal wave is related to the period T by the expression we can express the wave speed v in the alternative forms

RATE OF ENERGYTRANSFER BYSINUSOIDAL RATE OF ENERGYTRANSFER BYSINUSOIDAL WAVES ON STRINGS WAVES ON STRINGS As waves propagate through a medium, they transport energy. The total energy in one wavelength of the wave is the sum of the potential and kinetic energies: Where the potential energy is given by the integration

Where the kinetic energy is given by the integration Thus, the power, or rate of energy transfer, associated with the wave is

In fact: the rate of energy transfer in any sinusoidal wave is proportional to the square of the angular frequency ω and to the square of the amplitude A.