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Waves notes

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Introduction

WAVES AND SOUND image00.png

SUMMARY

Travelling wave characteristics

Waves transfer energy without transporting matter because each part of the medium oscillates on the spot.

The medium is the material that vibrates when a wave passes.

A transverse pulse causes the spring to move at right angles to the direction of motion of the pulse.

A longitudinal pulse causes the spring to move parallel to the direction of motion of the pulse.

A transverse wave is polarized when it vibrates in only one plane.

Longitudinal waves cannot be polarized.

Displacement is the position of a particle in a medium relative to its normal position.

Superposition : When two pulses over lap the total displacement at all points along the medium equals the sum of the individual displacements.

The speed of the particles of a medium is a maximum when their displacement is zero.

The speed of the particles of a medium is zero where the medium has maximum displacement.

The amplitude of a wave is the greatest distance the medium moves from its normal position.

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Middle

The particles in a compression and rarefaction have small displacements. The pressure is large or smaller than normal because the particles on opposite sides of the compression/rarefaction have opposite displacements.

The particle where the pressure is normal, has a maximum displacement.

Waves in two dimensions

The direction of propagation is at 90 degrees to the wavefront.

The angle of incidence or reflection is the angle between the direction of propogation and the normal.

The angle of incidence or reflection is the same as the angle between the wavefront and the barrier/boundary.

                                                        2.

Circular waves that reflect from a straight barrier seem to come from a point an equal distance behind the barrier.

Circular waves generated from the focus of a parabolic barrier, reflect as straight wavefronts.

Refraction of waves.

When waves move into a medium where they travel slower, the direction of propagation refracts towards the normal.

When refraction occurs, the speed and wavelength change but the frequency remains constant.

If the frequency of waves is increased, the amount of refraction decreases slightly - less deviation.

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Conclusion

Resonance occurs when a string/air column is stimulated by a vibration with the same frequency as one of its standing wave modes of vibration.

When resonance occurs, the amplitude of the standing wave is very large.

                                                              3.

Loudness and Intensity

Intensity in W/m2 measures the energy of the sound passing through an area of 1 m2 each second.

The intensity of sound that can just be heard is 10-12 W/m2.

Intensity is inversely proportional to the square of the distance. At twice the distance the intensity is one quarter as much.

Unit of Loudness is the Bel. A sound that can just be heard is 0 Bel

10 deciBel equals 1 Bel

Loudness in Bel equals log to the base 10 of the intensity divided by 10-12.

When loudness changes new loudness minus old loudness equals log to the base 10 of new intensity divided by old intensity.

Different frequencies at the same intensity are not heard to be the same loudness by the ear.

The ear is most sensitive when frequency is about 5000 Hz.

Two sounds have the same subjective loudness when they are heard by the ear to be equally loud.

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