Advanced Higher Physics Waves

Wave Properties 1 Displacement, y (unit depends on wave) Wavelength, λ (m) Velocity, v  v = f λ (ms -1 ) Period, T  T = 1 / f (s) Frequency, f  f = n / t (Hz) Amplitude, A (unit depends on wave) A

Types of Wave Transverse- displacement is perpendicular to direction of motion  e.g. water waves, e-m waves, wave on string, seismic ‘S’ waves Longitudinal - displacement is parallel to direction of motion  e.g. sound waves, seismic ‘P’ waves Link

Wave Properties 2 Intensity – (Irradiance)  I = P / A (W m -2 ) Coherence -  Wave on right have equal wavelength, frequency and amplitude Phase -  Waves are out of phase

Travelling Wave Equation Displacement, y, of a point on the wave is given by SHM equation- The wave travels at speed v from the source, so at a displacement, x, the disturbance arrives after a time - So at point x, the wave has the equation -

Travelling Wave Equation We can rearrange this if we substitute for v = f λ

Travelling Wave Equation N.B. we are taking the sine of the angle (ft - x/λ) - this is expressed in radians. Also note that at t = 0, y = 0 at point x = 0. If the wave is travelling in the opposite direction (i.e. right to left) its equation will be -

Example 1 A periodic wave travelling in the x-direction is described by the equation y = 0.2 sin (4  t - 0.1x) What are (a) the amplitude, (b) the frequency, (c) the wavelength, (d) the speed of the wave? (All quantities are in S.I. units.)

Example 2 For the previous wave, y = 0.2 sin (4  t - 0.1x) Calculate the displacement of the medium, y, caused by the wave at a point where x = 25 m when the time t = 0.30 s. Now do tutorial questions 1 to 6

Intensity The intensity of a wave is directly proportional to the square of its amplitude.

Transverse Speed and Acceleration Differentiate with respect to time to find velocity and acceleration in the y direction.

Phase Difference The phase difference between a particle at point p a distance x from the origin and the origin.  = 2  x p x The phase difference between any two points is  = 2  (x 2 – x 1 )

Stationary Waves Two waves with equal amplitude and wavelengths travelling in opposite directions. Phase change of  radians at surface. link Nodes – points where amplitude is always zero. Antinodes – points where there is maximum change in amplitude. Distance between nodes is /2

Experiment Link Now try making standing waves with rubber string, can you work out the speed of the wave? Answer tutorial questions 7 to 10

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