Homework SHM: Q2,3,4(a),6 Deadline: Day 4

1Wave propagation Mechanical waves Electromagnetic waves Require a medium to transmit energy? YesNo Examples Sound waves Waves in a slinky spring Light Radio waves

Direction of vibration Direction of travel of wave Direction of vibration Direction of travel of wave Transverse wavesLongitudinal waves Vibrations are at right angles to the direction of travel of the wave Vibrations are along the direction of travel of the wave ExamplesElectromagnetic waves, water waves ExamplesSound waves

Progressive / traveling waves Stationary / standing waves A disturbance moving from a source to surrounding places Energy is transmitted Energy is localized

Amplitude A: maximum disturbance measured from the resting position Wavelength : minimum distance in which a wave repeat itself Frequency f: number of waves produced in one second Period T: time taken for one wave to be produced (T = 1/f = 2  /  ) Resting position A C C C T T T

Wave speed v: distance traveled by a wave in one second. (v = f ) When waves travel along a string or spring, the wave speed is given by where T is the tension in the string or spring and m is its mass per unit length. This implies the wave speed can be increased if by stretching the string or spring more. Resting position A C C C T T T

Crest C: the peak of disturbance Trough T: the bottom of disturbance Note: 1.Speed of vibrating particles ≠ wave speed 2.Average speed of vibrating particles =. Resting position A C C C T T T

Displacement – distance graph and displacement – time graph Displacement – distance graph shows the displacements of all the particles on the wave at a certain time. Displacement – time graph shows the displacement of one particle at different times

Example 1     4 0 44 distance / cm displacement / cm travelling direction A BC D (a)Find the amplitude, and the wavelength of the wave. (b)If particle B performs 5 complete oscillations in 2 s, find the frequency and the speed of the wave.

Example 1     4 0 44 distance / cm displacement / cm travelling direction A BC D (c)At the instant shown, which of the particles A, B, C or D, is/are (i)momentarily at rest, (ii)moving upwards, and (iii)moving downwards?

Phase difference of particles in a wave displacement distance P Q Direction of wave TimePQ 0At restUpward ¼ TDownwardAt rest ½ TAt restDownward ¾ TUpwardAt rest T Upward

Phase difference of particles in a wave displacement distance P Q Direction of wave P leads Q by ¼ T or 90 o or  /2 radians

Phase difference of particles in a wave Vectors P’ and Q’ are rotating in anticlockwise direction with angular speed  where. The projections of vectors P’ and Q’ on the axis of displacement give the displacement time graphs of particles P and Q. Phase difference of P and Q is 90 o or  / 2 radians. P leads Q by 90 o or  / 2 radians. displacement distance P Q P’ Q’  Direction of wave