Lecture 1 - Waves and Fields Flashcards
Explain the Doppler Effect and Interference with regard to wave phenomena.
Doppler Effect: When a wave source and an observer are in motion relative to each other, the observed frequency of the wave changes. This phenomenon is known as the Doppler effect. When the source is approaching the observer, the observed frequency is higher than the actual frequency. Conversely, when the source is receding from the observer, the observed frequency is lower than the actual frequency.
Interference: When two or more waves overlap, they can interact with each other in a variety of ways. Constructive interference occurs when the peaks of two waves coincide, resulting in a wave with an enhanced amplitude. Destructive interference occurs when the peaks of one wave coincide with the troughs of another wave, resulting in a wave with a diminished amplitude.
What is the Doppler Effect?
It is the change in frequency of a wave in relation to an observer who is moving relative to the source of the wave.
What is Interference? Are there different types of interference?
Interference is a phenomenon that can be observed with all types of waves; it is a process by which two waves are superimposed, leading to a resultant wave that has either a higher or lower amplitude.
Constructive interference: When two superimposing waves are in-step or in-phase with each other.
Destructive interference: When two superimposing waves are in anti-phase which results in a full cancellation of the wave.
Examine the makeup of real-world signals using the Fourier Series and Fourier Transform.
Definition: Any function (x) which represents a periodic wave can be expressed as a combination of sine and cosine functions
Fourier Series: A Fourier series is a mathematical tool used to decompose a periodic signal into a sum of sine and cosine functions. These sine and cosine functions have fundamental frequencies and their multiples, which are called harmonics. The amplitude of each harmonic represents the relative strength of that frequency in the signal.
Fourier Transform: A Fourier transform is a mathematical tool used to decompose a non-periodic signal into a continuous superposition of complex exponentials. These complex exponentials have frequencies that range from negative infinity to positive infinity. The magnitude of each complex exponential represents the amplitude of that frequency in the signal, while the phase angle represents the phase of that frequency.
Application: Image processing, signal analysis (sound waves, music notes and electric signal), communication systems
What is the relationship between electricity and magnetism through Farday’s law of electromagnetic induction?
Changing a magnetic field induces an electromotive force (emf) in a conductor, which can drive an electric current. This phenomenon is the underlying principle behind many electrical devices, including generators, transformers, and motors.
In mathematical terms, this is “the induced EMF (or Voltage) in a closed circuit is equal to the rate of
change of magnetic flux.”
Convert the following values in scientific notation or use prefixes to simplify them.
(1) 2350
(2) 7,800,000,000
(3) 1,000,001
(4) 0.065
(5) 0.000098269
2350 = 2.35 x103
7,800,000,000 = 7.8 x109
1,000,001 = 1.000001 x106
0.065 = 6.5 x10-2
0.000098269 = 9.83 x10*-2
(2 d.p)
Write the 7 base quantities that make up the SI units.
Length - Meter m
Mass - Kilogram kg
Time - Second s
Electric Current - Ampere A
Temperature - Kelvin K
Amount of substance - Mole mol
Luminous intensity - Candela cd
Describe key wave parameters of amplitude, wavelength, frequency, and time period.
Amplitude: The maximum disturbance from its equilibrium position. This represents the power of the wave, so the larger the amp, the larger the power.
Wavelength: The distance in the graph over which the wave shape repeats itself and is measured as the distance between the same points in two adjacent waves.
Frequency: The number of oscillations (or wave cycles) per second. It is measured in Hz.
Time period: The time it takes for the wave pattern to advance a distance of one wavelength. It is reciprocal of the frequency, i.e., T = 1/f
Define the Newton unit of measurement.
One Newton is the force needed to accelerate one kilogram of mass at the rate of one meter per second squared in the direction of the applied force.
The unit of Newton’s are kg.m.s*-2
What is the speed [v] of a wave on a string when its mass density [μ] is 0.02 kgm-1 and it’s
pulled taught with a tension force [F] of 29.5 N.
38.4 ms-1
Use the equation where v = square root F/u; to show that the units of the wave speed [v] are of ms-1
.
ms-1 shown
Derive the equation for the velocity of a wave in terms of its frequency and wavelength using
the Speed-Distance-Time relationship
Shown.
Explain how a dog whistle works.
A dog whistle works by emitting sound in the ultrasonic range, which humans cannot hear, but dogs can.
The frequency of most dog whistles is within the range of 23 to 54 kHz, so they are above the range of human hearing, although some are adjustable down into the audible range.
To human ears, dog whistles only emit a quiet hissing sound.
A policeman clocks a driver speeding away from him with his Doppler radar gun at 45 ms-1
(just over a 100 mph). The Doppler radar gun operates using 8 GHz radio waves and the
policeman was stationary when taking the measurement. What is the frequency measured
by the radar gun? (Q5)
= 7.999998800 GHz
Waves fall into one of two categories: mechanical and electromagnetic.
What are mechanical and electromagnetic waves?
Mechanical waves: Travel within some type of material (a medium) that possesses the properties of (a) elasticity and (b) inertia.
Electromagnetic waves: Do no require a medium to travel through; they can simply travel through empty space as well as certain types of media. In a vacuum, all EM waves travel at the speed of light.
