Waves and Sound Notes

Waves and Sound Waves

  • A wave is a vibratory disturbance that moves through a medium.
    • Examples:
      • Mechanical waves (water waves, sound waves, waves on a spring)
      • Electromagnetic waves (light waves, microwaves, radio waves)

Types of Mechanical Waves

  • Transverse waves: Particles vibrate at right angles to the path along which the wave travels.
    • Crest: Maximum upward displacement.
    • Trough: Maximum downward displacement.
    • Wavelength: Distance between two corresponding points on the wave.
    • Amplitude: Resting position to max peak
  • Longitudinal waves: Particles vibrate in the direction parallel to the direction of motion of the wave.
    • Condensations: Areas of maximum compression.
    • Rarefactions: Areas of maximum separation.

Wave Properties

  • Frequency (f):
    • Unit: Hertz (Hz)
    • 1 Hz = 1 cycle/second
    • The number of vibrations executed by a particle each second.
  • Period (T):
    • Time taken for a particle to complete one cycle.
    • T = \frac{1}{f}
  • Wavelength ($\lambda$):
    • Distance along the direction of propagation between corresponding points on the wave.
  • Amplitude (A):
    • Maximum displacement of any particle in the medium relative to its rest position.

Wave Velocity (V)

  • The distance through which each wave moves per second.
  • V = f\lambda

Velocity of a Transverse Wave on a Stretched String or Cord:

  • V = \sqrt{\frac{T}{m/L}}
    • T = Tension in the cord
    • m = Mass of the cord
    • L = Length of the cord

Fundamental Frequency of Stretched String

  • f = \frac{1}{2L} \sqrt{\frac{T}{m/L}}

Laws of Vibrating String

  • The Law of Length:
    • The frequency of a vibrating string is inversely proportional to its length, other factors being the same.
    • f1 L1 = f2 L2
  • The Law of Tension:
    • The frequency of a vibrating string is directly proportional to the square root of the tension, other factors being the same.
    • \frac{f1}{\sqrt{T1}} = \frac{f2}{\sqrt{T2}}
  • The Law of Diameter:
    • The frequency of a vibrating string is inversely proportional to its diameter, other factors being the same.
    • f1 d1 = f2 d2
  • The Law of Density:
    • The frequency of a vibrating string is inversely proportional to its density, other factors being the same.
    • f1 \rho1 = f2 \rho2

Sound Waves

  • Compressional waves in a material medium (air, water, steel).
  • Compressions and rarefactions striking the eardrum result in the sensation of sound.

Nature of Waves

  • Infrasonic waves: Frequencies below 20 Hz.
  • Ultrasonic waves: Frequencies above 20 kHz.
  • Sonic or Sound waves: Frequencies from 20 Hz to 20kHz.

SOUND CHARACTERISTICS

  1. Intensity of sound: Power carried by the wave through a unit area perpendicular to the direction of propagation.
    • Increased by increasing the amplitude and the area of the vibrating body.
    • Depends on the distance of the source from the ear and the density of the medium.
  2. LOUDNESS: Strength of the sensation as received by the ear. Depends on the amplitude of the vibrations.
  3. PITCH: Property of sound that depends on the frequency of the waves received by the ear.
  4. QUALITY or TIMBRE: Characteristics of sound that enable distinguishing between sounds produced by different sources. Depends on the waveform or the number and kind of overtones that accompany the fundamental.

SOUND INTENSITY LEVEL EQUATIONS

  • I = 10 \log \frac{I}{I_0}
    • Units: W/m^2
    • I_0 = 10^{-12}

SOUND VELOCITY EQUATIONS:

  • Speed of sound in air:
    • v = 331 + 0.6t
      • t = temperature of air in °C
  • The speed of sound is independent of pressure, frequency, and wavelength

DOPPLER’S EFFECT

  • Apparent rise and fall in the pitch of the sound of a sounding body or observer approaches and as it leaves the observer or sounding body.
    • Case 1: Moving source- Stationary Observer
    • Case 2: Stationary source- Moving Observer
    • Case 3: Moving Source- Moving Observer

Communication

Basic Principle

  • Electronic Communication: Transmission, reception, and processing between two or more locations using electronic circuits.
  • Allocation: Entry in the table of frequency allocations of a given frequency band for use by one or more terrestrial or space radio communication services or the radio astronomy service under specified conditions.
  • Allotment: Entry of a designated frequency channel in the agreed plan, adopted by the ITU, for use by one or more nations for terrestrial or space radio communication services in one or more identified countries or geographic areas and under specified conditions.
  • Assignment: Authorization given by a nation for a radio station to use a radio-frequency channel under specified conditions.

History Perspective

  • 1820 – Hans Christian Oersted: Discovered the relation between electricity and magnetism (electromagnetism).
  • 1821- Andre Marie Ampere : Observed momentarily the phenomenon we now call electromagnetic induction and hypothesized the existence of magnetic field around a current- carrying conductor.
  • 1822 – Michael Faraday: Discovered electromagnetic induction.
  • 1830 – Joseph Henry: Demonstrated telecommand by sending an electronic current over one mile of wire to activate an electromagnet which caused a bell to strike; thus, wire telegraphy was born.
    • Samuel F.B. Morse: Successfully exploited Henry’s invention commercially.
  • 1866 – James Clerk Maxwell: Put together the principles of Oersted, Faraday, and hypothesized the existence of electromagnetic waves.
  • 1886 – Heinrich Hertz: Performed an experiment on spark gap transmission verifying Maxwell's statement; showed the existence of radio waves that paved the way for wireless communication.
  • 1896 – Guglielmo Marconi: Developed the first wireless telegraph and successfully sent a message over a few kilometers using a spark gap transmitter.
  • 1990 – Reginald Audrey Fessenden: Invented AM and successfully transmits a few words using spark gap transmitter.
  • 1936 – Major Edwin Armstrong: Developed the first successful FM radio system.

Elements of Basic Communications System

  • Transmitter: A collection of electronic components and circuits designed to convert the information or intelligence into a signal suitable for transmission over a given communication medium.
  • Channel: The medium by which the electronic/electromagnetic signal is sent from one place to another.
    • Wire Medium: The signal is confined within the proximity of the channel or medium (Bounded or Guided Medium).
    • Wireless Medium: The signal is not subjected to limits, boundaries, or channel restrictions (Unbounded or Unguided Medium).
    • Noise: A random, undesirable electrical energy that enters the communication system and interferes with the transmitted message.
  • Receiver: Another collection of electronic components and circuits that accept the transmitted message from the channel and convert it back into a form understandable by humans.

Characteristics of Noise

  • Unwanted
  • Disturbs
  • Interfere
  • Affects
  • Undesired
  • Cannot be eliminated but just minimize

Types of Noise

  • External: Introduced in the medium/channel and difficult to quantify.
  • Internal: Produced at the receiver resistor, diodes, transistor, wires.

Types External Noise

  • Industrial/man-made noise:
    • Occurs randomly at frequencies up to 600MHz.
    • Common sources: Fluorescent lights, ignition systems of engines, switching equipment, commutators of electric motors, leakage from high voltage transmission lines.
  • Atmospheric/Static noise:
    • Caused by lighting discharges during thunderstorms and other natural electrical disturbances occurring in Earth’s atmosphere.
    • Less severe above 30 MHz.
  • Extraterrestrial/space Noise:
    • Can be observed between 8 MHz to 1.5 GHz.
    • Common sources: Sun (constant noise radiation, sunspots), stars, and galaxies.

Types Internal Noise

  • Thermal Noise
  • Shot Noise
  • Transit Time Noise
  • Flicker Noise
Types Internal Noise Details
  • Thermal Noise:
    • Also called Brownian noise.
    • Also called Johnson noise.
    • Also called white noise (spread throughout the usable spectrum).
    • Associated with the rapid and random movement of electrons within a conductor due to thermal agitation.
    • Primary source is resistor.
  • Shot Noise:
    • Caused by the random arrival of carriers at the output element of an electronic device, such as a diode, FET, or BJT.
  • Transit Time Noise:
    • Caused by the transit-time effect that occurs when the time taken by an electron to travel from the emitter to the collector of a transistor becomes comparable to the period of the signal being amplified.
    • Has a greater effect at higher frequencies, particularly in the microwave region.
    • Also called high-frequency noise.
  • Flicker Noise:
    • Noise found at low audio frequencies in transistors.
    • Proportional to the emitter current and junction temperature.
    • Inversely proportional to frequency and completely negligible at about 500 Hz.
    • Another name: Low frequency noise, modulation noise, excess noise, pink noise, 1/f noise.

Noise Spectrum

  • White Noise
  • Pink Noise
  • Brown Noise
  • Blue Noise
  • Purple Noise
  • Orange Noise
  • Black Noise
Noise Spectrum Details
  • White Noise: Has an equal amount of energy per frequency.
  • Pink Noise: Has an equal amount of energy per octave.
  • Brown Noise: Similar to pink noise, but with a power density decrease of 6dB per octave with increasing frequency (density proportional to 1/f^2) over a frequency range which does not include DC.
  • Blue Noise: The opposite of pink noise; it doubles the amount of energy each time you go up 1 octave.
  • Purple Noise: Power density increases 6 dB per octave with increasing frequency (density proportional to f^2) over a finite frequency range.
  • Orange Noise: Quasi-stationary noise with a finite power spectrum with a finite number of small bands of zero energy dispersed throughout a continuous spectrum.
  • Black Noise: Has a frequency spectrum of predominately zero power level over all frequencies except for a few narrow bands or spikes.

MODULATION

  • Is the process of varying a carrier signal, typically a sinusoidal signal, to use that signal to convey information.
  • The three key parameters of a sinusoidal are its amplitude, its phase, and its frequency.

Modulation Types

  1. Analog Modulation
  2. Digital Modulation
  3. Hybrid Modulation

WAVEFORM REPRESENTATION

  1. Time Domain
  2. Frequency Domain

Time Domain

  • A standard oscilloscope is used to display the amplitude versus time representation of the input signal.
  • Displays: Amplitude, Time, Frequency, Wavelength, Period
Time Domain Definitions
  • Frequency: The number of times a particular phenomenon occurs in each period expressed in Hertz.
  • Wavelength: The distance between two points of similar cycles of a period wave or the distance traveled by an electromagnetic wave during the time of one cycle typically expressed in meters.
  • Period: The time required for one complete cycle of a repetitive system, or simply the reciprocal of frequency.
Relationship between wavelength, Frequency and Period
  • \lambda = \frac{c}{f}
  • f = \frac{c}{\lambda}
  • T = \frac{1}{f}
  • f = \frac{1}{T}
  • c = 3 \times 10^8

Frequency Domain

  • A spectrum analyzer is used to display the amplitude versus frequency representation of the input signal.

DOPPLER EFFECT

  • A perceived change of frequency of a wave as the distance between the source and the observer changes.

Doppler Frequency of Sound Waves

  • f0 = fs \frac{v \pm v0}{v \pm vs}
  • f0 = fs
  • f0 = fs

Doppler Frequency of Electromagnetic Wave

  • f0 = fs \sqrt{\frac{1 \pm \frac{v}{c}}{1 \pm \frac{v}{c}}}
  • c = 3 \times 10^8 m/s

Operational Words Code

  • Roger: I received your message
  • Over: I have completed transmitting and wait your reply
  • Go ahead: Same as over
  • Out: I have completed my communication and do not expect to transmit again.
  • Clear: I have no further traffic (sometimes use in place of Out)
  • Stand by: Wait for another call or further instructions
  • Break: I am changing from one part of the message to another (also used to request received operator to indicate if he has received the portion of the message transmitted thus far)
  • Copy: Respond to Break

International Phonetic Alphabet

  • A - Alpha
  • B - Bravo
  • C - Charlie
  • D - Delta
  • E - Echo
  • F - Foxtrot
  • G - Golf
  • H - Hotel
  • I - India
  • J - Juliet
  • K - Kilo
  • L - Lima
  • M - Mike
  • N - November
  • O - Oscar
  • P - Papa
  • Q - Quebec
  • R - Romeo
  • S - Sierra
  • T - Tango
  • U - Uniform
  • V - Victor
  • W - Whiskey
  • X - X-ray
  • Y - Yankee
  • Z - Zulu