Waves Topic 4 5 Wave Properties Wave Behaviour

Waves Topic 4. 5 Wave Properties

Wave Behaviour v. Reflection in one dimension

This diagram shows a pulse travelling along a string

This diagram shows the pulse after it has been reflected

Notice v The pulse keeps its shape v It is inverted v It has undergone a 180 o phase change v Or change in phase

v This is because the instant the pulse hits the fixed end, the rope attempts to move the fixed end upwards v It exerts an upwards force on the fixed end v By Newton’s third law, the wall will exert an equal but opposite force on the rope v This means that a disturbance will be created in the rope which, however is downwards and will start moving to the left

v If the end of the rope is not fixed but free to move the situation is different v Most of the pulse would carry on in the same direction, some would be reflected but the reflected pulse is in the same phase as the original pulse v There is a change of direction, but no inversion here

v. Similar situations occur in springs and columns of air

Wave Behaviour v. Reflection in two dimensions

v. Light is shone from above a ripple tank onto a piece of white card beneath v. The bright areas represents the crests v. The dark areas represent the troughs

v. These wavefronts can be used to show reflection (and refraction and diffraction and interference) of water waves

Normal Angle of incidence = Angle of reflection

The Law for Reflection • The angle of incidence is equal to the angle of reflection • Also - The incident ray, the reflected ray and the normal lie on the same plane • Use this rule for any ray or wave diagram involving reflection from any surface

• For circular waves hitting a flat reflector, the reflected waves appear to come from a source, which is the same distance behind the reflector as the real source is in front of it • Also a line joining these 2 sources is perpendicular to the reflecting surface

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• If a plane wave is incident on a circular reflector then the waves are reflected so that they – Converge on a focus if the surface is concave – Appear to come from a focus if the surface is convex

Echos • In the case of sound, a source of sound can be directed at a plane, solid surface and the reflected sound can be picked up by a microphone connected to an oscilloscope. • The microphone is moved until a position of maximum reading on the oscilloscope is achieved. • When the position is recorded it is found that again the angle of incidence equals the angle of reflection.

Wave Behaviour v. Refraction

• The speed of a wave depends only on the nature and properties of the medium through which it travels. • This gives rise to the phenomenon of refraction • Refraction is the change of direction of travel of a wave resulting from a change in speed of the wave when it enters the other medium at an angle other than right angles.

• In a ripple tank this is achieved by using a flat piece of plastic, giving two regions of different depth • As the wave passes over the plastic it enters shallow water and slows down. • As v = f , • if v decreases • And f is constant (the source hasn’t changed) • must also decrease • So the waves get closer together

• If the waves enter the shallow area at an angle then a change in direction occurs. Shallow water

• This is because the bottom of the wavefront as drawn, hits the shallow water first so it slows, and hence travels less distance in the same time as the rest of the wavefront at the faster speed travel a larger distance!

• If the waves enter the deep area at an angle then a change in direction occurs Deep water

• This is because the top of the wavefront hits the deep water first so it speeds up, and hence travels more distance in the same time as the rest of the wavefront at the slower speed travel a smaller distance!

Refraction for light Refracted ray Partial reflection Refracted ray Incident ray

Snell’s Law • Snell discovered that for any two media • Sin 1 / Sin 2 = constant • Also v 1 / v 2 = the same constant • Where 1 is the angle of incidence in the 1 st medium, v 1 is the velocity in that medium • And 2 is the angle of refraction in the second medium, v 2 is the velocity • The constant is 1 n 2

• Therefore 1 n 2 = sin 1 = v 1 sin 2 v 2

• This law enable us to define a property of a given optical medium by measuring 1 and 2 when medium 1 is a vacuum • The constant is then the property of medium 2 alone and it is called the refractive index (n). • We usually write • n = (Sin i) / (Sin r) • n is also a ratio of the speeds in the 2 mediums i. e. n = cvacuum / vmedium

Using Refractive Index • Refractive index is written for materials in the form of light entering from a vacuum or air into the material. • The refractive index of a vacuum or air is 1 • It can also be shown that, for two mediums (1 and 2) • n 1 sin 1 = n 2 sin 2 • Care needs to be taken when dealing with light leaving a material

Combining them! • Rearranging n 2/n 1 = sin 1 / sin 2 • But n 1 = 1 • n 2 = sin 1 / sin 2 • Therefore anb = nb / na

Refraction of Sound • A sound wave is also able to be refracted. • This is due to the fact that the speed of sound is affected by temperature and the medium through which it travels.

Diffraction • Diffraction is the spreading out of a wave as it goes passed an obstacle or through an aperture • When the wavelength is small compared to the aperture the amount of diffraction is minimal • Most of the energy associated with the waves is propagated in the same direction as the incident waves.

• When the wavelength is comparable to the opening then diffraction takes place. • There is considerable sideways spreading, i. e. considerable diffraction

• Diffraction also takes place when a wave moves passed an obstacle • If the wavelength is much smaller than the obstacle, little diffraction takes place • If the wavelength is comparable to the obstacle size, then diffraction takes place

Using Huygens’ Principle • Remember that Huygens' idea was to consider every single point on the wavefront of the wave as itself a source of waves. • In other words a point on the wavefront would emit a spherical wavelet or secondary wave, • of same velocity and wavelength as the original wave.

• Therefore as a wave goes through a gap or passed an obstacle the wavelets at the edges spread out. • Huygens’ construction can be used to predict the shapes of the wave fronts.

• The new wavefront would then be the surface that is tangent to all the forward wavelets from each point on the old wavefront. • We can easily see that a plane wavefront moving undisturbed forward easily obeys this construction.

The Principle of Linear Superposition • Pulses and waves (unlike particles) pass through each other unaffected and when they cross the total displacement is the vector sum of the individual displacements due to each pulse at that point. • Try this graphically with two different waves

Interference • Most of the time in Physics we are dealing with pulses or waves with the same amplitude. • If these cross in a certain way we will get full constructive interference, here the resultant wave is twice the amplitude of each of the other 2 + =

• If the pulses are 180 o ( ) out of phase then the net resultant of the string will be zero. This is called complete destructive interference. + =