Progressive Waves PDF

PROGRESSIVE WAVES A progressive wave is a wave that transfers energy from one location to another. Eg. Water waves- progressive transverse wave Sound waves – progressive longitudinal wave As a wave moves in a particular direction, energy is transferred in that same direction. This energy is rela...

PROGRESSIVE WAVES A progressive wave is a wave that transfers energy from one location to another. Eg. Water waves- progressive transverse wave Sound waves – progressive longitudinal wave As a wave moves in a particular direction, energy is transferred in that same direction. This energy is related to the intensity of the wave which is related to the amplitude of the wave I α A2 I = kA2 The intensity of the wave is directly proportional to the square of the amplitude of the wave. This means that a wave with large amplitude will transmit much more energy than a wave with smaller amplitude. STATIONARY WAVES Stationary waves are formed by the superposition of two progressive waves of the same type , of equal frequency and amplitude travelling with the same speed in opposite directions. Both longitudinal and transverse waves can form stationary waves. When two coherent, progressive waves superimpose, a stationary wave is produced. Stationary wave produced on a string A stationary wave can be produced on a string by causing it to oscillate rapidly. One length of a string is attached to a mechanical oscillator. The string passes over a frictionless pulley and is kept taut by using small weights. The oscillator produces the progressive waves, which travel from left to right. The reflected waves then superimpose with the produced, incident waves and produces a stationary wave. The velocity of the incident wave is given by : There are points along a stationary wave where the particles are permanently at rest. These points are called nodes. The displacement at these points is zero. At points midway between the nodes on a stationary wave, the displacement is twice the amplitude of either progressive wave. These points are called antinodes. Kundt’s tube The speed of sound can be measured using a long cylindrical tube with one end open and the other closed. The tube is filled with a fine powder. A loudspeaker, connected to a signal generator is placed at the open end. The frequency of the signal generator is adjusted so that the powder eventually settles. The sound inside the tube eventually creates a stationary wave and the powder settles at the displacement nodes. For measuring this displacement, the wavelength of the wave can be found and the speed of sound can be determined Sound waves Ultra sound – high freq sound > 20, 000 Hz Medicine – to observe fractures, size of feotus, clean medical equipment Navigation – depth Industry – hairline fractures in mechanical components, underlying earth structures. Sound waves and musical instruments Pitch - frequency Loudness- amplitude Quality Fundamental frequency – lowest frequency that a vibrating string or pipe can produce Usually notes of higher frequencies than the fundamental is produced together with the fundamental frequency. These notes are called overtones. Stationary waves in an open ended tube Stationary waves in a closed pipe system ( one end open) eg resonance tube Resonance tube A resonance tube is used to determine the speed of sound. A tuning fork of known frequency is placed over the air column. A longitudinal wave is transmitted down the tube and reflected when it hits the surface of the water. The two waves super impose and produce a stationary wave. Depending on the length of the air column, only certain modes of vibration is possible. If the fundamental mode of vibration is equal to the frequency of the tuning fork, resonance occurs. Example f = 400 Hz Resonance occurring at 21 cm, then at 64 cm Wavelength of light waves –Visible spectrum 4- 7 x 10-7 m 400 – 700 nm LIGHT WAVES Diffraction Diffraction through a single slit When a single slit is placed in front of a parallel beam of light, diffraction occurs. The following is observed For a diffraction grating element It consists of large numbers of equally spaced lines ruled on a piece of glass or plastic. When monochromatic light is incident at right angles to the grating, an interference pattern of bright and dark fringes are observed. dsinθ = nλ d= thickness of one of the lines etched onto the element 600 lines per mm 600, 000 lines per m Thickness of 1 = d = 1/600,000 = June 2008 (i)dsineθ = nλ sine θ = 1 590nm > 589 nm d = nλ no. 0f lines per m = 6 x 105 d = 1/ 6 x 105 = 1.67 x 10-6 n = 1.67 x 10-6/590 x 10-9 = 2.8 Max number of orders = 2 (ii) dsineθ = nλ 1.67 x 10-6 x sine θ = 2 x 589 x 10-9 Θ = 44.860 dsineθ = nλ 1.67 x 10-6 x sineθ = 2 x 590 x 10-9 Θ = 44.96 Angular separation = 44.96 – 44.86 = 0.100 Interference Young’s Double Slit Expt Conditions 1. Waves must be coherent 2. Same amplitude 3. Waves must be polarized