Waves And the Oscillations Course in Physics
- 3. DEFINITION •A transverse wave is mechanical wave in which all points on a wave oscillate along paths at right angles(perpendicular) to the direction of the wave's direction of travel. •Examples: water waves, seismic waves, electromagnetic waves, light waves etc.
- 4. SHAPE OF WAVE • Transverse wave (wave on string) is completely described by the sinusoidal function that gives the shape of the wave i.e. Y(x,t)=Ym sin(kx-ωt) • A sinusoidal function is a mathematical curve that describes a smooth periodic curve/ oscillation. It begins to repeat itself when its angle is increased to 2π rad(1 cycle).
- 5. WAVEFORM OF TRANSVERSE WAVE
- 6. EQUATION OF TRANSVERSE WAVE Following equation describes a transverse wave: Y(x,t)=Ym sin(kx-ωt) where Y(x,t) = Displacement Ym = Amplitude (kx - wt) = Phase K = AngularWave Number W = Angular Frequency X = position, t = time
- 7. WAVELENGTH • Wavelength is the distance between identical points in the adjacent cycles of a waveform signal propagated along a wire. • Its symbol is λ. • Formula for wavelength of wave is λ= v/f • Its unit is meter. • It is inversely related to the frequency of the wave.
- 8. • Amplitude is defined as magnitude of maximum displacement of string element (position) from equilibrium position. • It is represented byYm and its unit is meter. • The amplitude of the wave determines the extremes of element’s displacement. AMPLITUDE ()
- 9. ANGULAR FREQUENCY • Angular frequency is defined as number of cycles per unit time. • The angular frequency refers to the angular displacement per unit time and is calculated from the frequency with the equation =2πf ω • The unit of angular frequency is rad/sec
- 10. ANGULAR WAVENUMBER • Angular wavenumber(k) is simply the reciprocal of the wavelength, given by the expression. k = 1 / λ • The wavenumber (k) is therefore the number of waves or cycles per unit distance. • Its unit is radian per meter or 1/m
- 11. PHASE • Phase is defined as the relationship between the position of the amplitude crests and troughs of two waveforms. • Phase can be measured in distance, time, or degrees. • Phase is determined using relation (kx – ωt) With k= wave no, x= displacement, ω= frequency and t=time • If the peaks of two waves with the same frequency are in exact alignment at the same time, they are said to be in phase. Conversely, if the peaks of two waves with the same frequency are not in exact alignment at the same time, they are said to be out of phase.