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Tutorial 2 Electromagnetic wave equation 1.1 A harmonic disturbance of amplitude 10 units is described by a wave function ?(x,t) such that ?(0,0) = 0. If the wave has an angular frequency of ?/2 and moves with a speed of 10 m/s, determine: a) the wavelength; b) the disturbance magnitude at t = 3 s, at a point which is 20 m from the origin. 1.2 The disturbance at t = 0 of a plane harmonic wave is given by ?(z,0) = 5 sin(? z / 25). If the wave is moving in the negative z-direction at a speed of 2 m/s, write an expression for the disturbance at t = 4 s. 1.3 a) Write the equation of a harmonic wave traveling along the y-direction at t = 0 if it is known to have an amplitude of 5 m and a wavelength of 50 m. Write an expression for the disturbances at t = 4 s if the wave is moving in the negative y-direction at a speed of 2 m/s. 1.4 A light wave propagates from point A to point B in air. If a glass plate (n_g = 1.5) of thickness l = 1 mm is introduced in its path, by how much will that alter the phase of the wave at point B, knowing that ?0 = 500 nm? 1.5 The magnetic field induction of a plane electromagnetic harmonic wave is given by the equation: B = 66.7 × 10^?8 û_y sin[4? × 10^6 (t ? 3 × 10^8 z)] (SI units). a) Find the refractive index of the material in which the wave propagates. b) Write an expression for the corresponding electric field intensity. What are the wavelength, speed and direction of motion of the disturbance? 1.6 For a harmonic wave given by y = 10 sin(628.3 x ? 6283 t), with x and y in centimeters and t in seconds, determine: a) wavelength, b) frequency, c) propagation constant (k), d) angular frequency, e) period, f) velocity, g) amplitude. 1.7 An electromagnetic wave of frequency 6? × 10^14 s^?1 sweeps across the room with a speed essentially equal to that in vacuum. If the difference in phase between two points at a given instant is ?/3, what can you say about their separation in space? 1.8 The rate at which the phase of a sinusoidal wave changes in time, at any given point in space, is 12? × 10^4 rad/s and the rate at which the phase changes with distance x, at any given time, is 4? × 10^6 rad/m. Write an expression for the wave function, provided that the initial phase is ?/3, the amplitude is 10 and the wave advances in the positive z-direction. What is its speed?

          Tutorial 2

Electromagnetic wave equation

1.1 A harmonic disturbance of amplitude 10 units is described by a wave function ?(x,t) such that ?(0,0) = 0. If the wave has an angular frequency of ?/2 and moves with a speed of 10 m/s, determine: a) the wavelength; b) the disturbance magnitude at t = 3 s, at a point which is 20 m from the origin.

1.2 The disturbance at t = 0 of a plane harmonic wave is given by ?(z,0) = 5 sin(? z / 25). If the wave is moving in the negative z-direction at a speed of 2 m/s, write an expression for the disturbance at t = 4 s.

1.3 a) Write the equation of a harmonic wave traveling along the y-direction at t = 0 if it is known to have an amplitude of 5 m and a wavelength of 50 m. Write an expression for the disturbances at t = 4 s if the wave is moving in the negative y-direction at a speed of 2 m/s.

1.4 A light wave propagates from point A to point B in air. If a glass plate (n_g = 1.5) of thickness l = 1 mm is introduced in its path, by how much will that alter the phase of the wave at point B, knowing that ?0 = 500 nm?

1.5 The magnetic field induction of a plane electromagnetic harmonic wave is given by the equation: B = 66.7 × 10^?8 û_y sin[4? × 10^6 (t ? 3 × 10^8 z)] (SI units). a) Find the refractive index of the material in which the wave propagates. b) Write an expression for the corresponding electric field intensity. What are the wavelength, speed and direction of motion of the disturbance?

1.6 For a harmonic wave given by y = 10 sin(628.3 x ? 6283 t), with x and y in centimeters and t in seconds, determine: a) wavelength, b) frequency, c) propagation constant (k), d) angular frequency, e) period, f) velocity, g) amplitude.

1.7 An electromagnetic wave of frequency 6? × 10^14 s^?1 sweeps across the room with a speed essentially equal to that in vacuum. If the difference in phase between two points at a given instant is ?/3, what can you say about their separation in space?

1.8 The rate at which the phase of a sinusoidal wave changes in time, at any given point in space, is 12? × 10^4 rad/s and the rate at which the phase changes with distance x, at any given time, is 4? × 10^6 rad/m. Write an expression for the wave function, provided that the initial phase is ?/3, the amplitude is 10 and the wave advances in the positive z-direction. What is its speed?

$Tutorial 2 Electromagnetic wave equation 1.1 A harmonic disturbance of amplitude 10 units is described by a wave function ?(x,t) such that ?(0,0) = 0. If the wave has an angular frequency of ?/2 and moves with a speed of 10 m/s, determine: a) the wavelength; b) the disturbance magnitude at t = 3 s, at a point which is 20 m from the origin. 1.2 The disturbance at t = 0 of a plane harmonic wave is given by ?(z,0) = 5 sin(? z / 25). If the wave is moving in the negative z-direction at a speed of 2 m/s, write an expression for the disturbance at t = 4 s. 1.3 a) Write the equation of a harmonic wave traveling along the y-direction at t = 0 if it is known to have an amplitude of 5 m and a wavelength of 50 m. Write an expression for the disturbances at t = 4 s if the wave is moving in the negative y-direction at a speed of 2 m/s. 1.4 A light wave propagates from point A to point B in air. If a glass plate (ng = 1.5) of thickness l = 1 mm is introduced in its path, by how much will that alter the phase of the wave at point B, knowing that ?0 = 500 nm? 1.5 The magnetic field induction of a plane electromagnetic harmonic wave is given by the equation: B = 66.7 × 10^?8 ûy sin[4? × 10^6 (t ? 3 × 10^8 z)] (SI units). a) Find the refractive index of the material in which the wave propagates. b) Write an expression for the corresponding electric field intensity. What are the wavelength, speed and direction of motion of the disturbance? 1.6 For a harmonic wave given by y = 10 sin(628.3 x ? 6283 t), with x and y in centimeters and t in seconds, determine: a) wavelength, b) frequency, c) propagation constant (k), d) angular frequency, e) period, f) velocity, g) amplitude. 1.7 An electromagnetic wave of frequency 6? × 10^14 s^?1 sweeps across the room with a speed essentially equal to that in vacuum. If the difference in phase between two points at a given instant is ?/3, what can you say about their separation in space? 1.8 The rate at which the phase of a sinusoidal wave changes in time, at any given point in space, is 12? × 10^4 rad/s and the rate at which the phase changes with distance x, at any given time, is 4? × 10^6 rad/m. Write an expression for the wave function, provided that the initial phase is ?/3, the amplitude is 10 and the wave advances in the positive z-direction. What is its speed?$

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