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CAS Physics Test #1 Study Guide

Vocabulary and Concepts

  • Matter:
    Defined as any substance that has both mass and volume.

  • Energy:
    The ability to do work.

  • Work:
    To cause change.

  • 1st Law of Thermodynamics:
    Known as the "Law of Conservation of Energy" - states that energy can neither be created nor destroyed; it can only change forms.

  • 2nd Law of Thermodynamics:
    Referred to as the "Law of Entropy" - indicates that as energy changes forms, it becomes less useful and more disordered.

  • Entropy:
    Represents the notion that "things tend to fall apart."

  • Implications of the Laws of Thermodynamics:

    • The total energy of the Universe is assumed to be constant.

    • All energy in the Universe was released by the Big Bang approximately 13.8 billion years ago.

    • As the Universe evolves, it becomes more disordered. For example, galaxies spread further and further apart.

    • The transfer of energy from one form to another converts some energy into less usable forms, such as the conversion of chemical energy in food to thermal energy that escapes from the body.

  • E = mc²:

    • This is Einstein’s famous equation from his Theory of Special Relativity.

    • It led Einstein to view matter as "concentrated energy" and illustrated that mass and energy are interchangeable, which has implications for the development of nuclear bombs.

  • Energy Waves:

    • All energy waves travel as repeated oscillation patterns throughout the universe.

    • Some energy waves, like sound waves, require a medium to pass through, while others, such as light waves, can travel through the vacuum of space.

  • Sinusoidal Waves:

    • These are individual energy waves that can be mathematically analyzed as sine/cosine curves.

  • Longitudinal Waves:

    • These energy waves oscillate parallel to the direction of wave motion.

    • Sound waves are examples of pressure waves traveling through a medium, causing particles of the medium to alternatively compress and stretch, producing a repetitive wave cycle.

  • Compressions:

    • Locations in a medium where particles are compressed together due to a pressure wave.

  • Rarefactions:

    • Locations where particles of a medium are stretched apart by a pressure wave.

  • Transverse Waves:

    • Energy waves that oscillate perpendicular to the direction of wave motion.

    • Water waves serve as an example of transverse energy waves, where water particles move up and down as energy waves pass through, creating crests and troughs.

Wave Concepts/Variables/Vocabulary

  • Wavelength (E):

    • The length of one complete sinusoidal wave, measured in meters (m).

  • Crest:

    • The highest part of the wave.

  • Trough:

    • The lowest part of the wave.

  • Nodes:

    • Stationary points in standing waves that serve as center points.

  • Antinodes:

    • The highest (crest) and lowest (trough) parts of the wave.

  • Amplitude:

    • The vertical distance between a node and an antinode, which determines the intensity of the wave.

    • For sound waves, amplitude is described as intensity, "I," measured in Watts/meter².

  • Frequency (Q):

    • The number of waves passing a given point per second, measured in Hertz (Hz).

    • Example: 120 Hz indicates 120 waves passing a point per second.

  • Period (T):

    • The time, in seconds (s), it takes for one complete wave to pass a designated point.

  • Wave Speed (v):

    • The speed of a wave, measured in meters/second (m/s).

Wave Interference

  • Constructive Interference:

    • Occurs when two identical waves are perfectly in phase, meaning the crests and troughs are synchronized, creating a new wave with twice the original amplitude through a process called "amplification."

  • Destructive Interference:

    • Occurs when two identical waves are perfectly out of phase, meaning the crest of one wave aligns with the trough of another, cancelling each other out in a process labeled "extinction."

  • Standing Waves and Resonance:

    • Resonance: When reflecting waves combine, they exhibit constructive interference, increasing amplitude with each reflection.

    • Standing Waves: These occur when an energy wave reflects back upon itself causing oscillation perpendicular to the wave direction with high amplitude, often seen in two attached endpoints such as strings or bridges.

    • Resonant Frequencies: An object has a natural resonant frequency of vibration; matching an incoming wave's frequency causes resonance, which can lead to the object's breakage at high resonances.

    • Example: The Tacoma-Narrows Bridge collapse highlighted the consequences of resonance, as does the spectacle of glass breaking in demonstrations.

Harmonic Series

  • Harmonic Series:

    • Formed when standing waves generate multiple harmonic frequencies that are integer divisions of the initial wavelength.

Standing Waves on Strings

  • Fundamental Wavelength:

  • The wavelength of the first harmonic wave on a string.

  • The fundamental frequency is calculated as twice the string length.

    • Fundamental Frequency:

  • The frequency of the 1st harmonic wave on a string. The pitch perceived by the human brain is based solely on this frequency.

    • Formulas Related to Harmonic Series:

  • Ensure understanding of how to compute wavelengths and frequencies within harmonic series, especially in strings.

  • Wave Speed on a String: Determined by two factors:

  • Force of Tension (FT): The greater the tension force (due to stretching), the faster a wave travels through the string, leading to higher frequencies and pitch.

  • Linear Mass Density (7): Defined as mass per length, measured in kg/m. A higher linear mass density increases resistance to vibration, resulting in a lower fundamental frequency and pitch.

  • Formula: 7 = \frac{m}{L} where (m) is mass and (L) is length.

Sound Intensity vs. Loudness

  • Sound Intensity:

    • Measures how much power is transmitted by a sound wave at various distances, calculated in Watts/meter². Sound waves move outward in spherical shells whose total surface area is described by A = 4\pi r^2.

  • Loudness:

    • A perception created in the brain based on electrical signals; not an inherent quality of sound. Loudness is quantified in decibels (dB).

    • An increase of 10 dB is perceived as a sound being ten times louder, for example, a 60 dB sound is 10,000 times louder than a 20 dB sound.

    • Prolonged exposure to high dB sounds can lead to ear damage or even death.

    • Formulas:

    • I = \frac{P}{A} or I = \frac{1}{2} \rho v \omega^2 A^2, where $

  • dB = 10 \log{\frac{I}{I_0}}$.

Soundwave Facts

  • Sound does not exist as a tangible entity; it is an energy pressure wave that causes vibration in the eardrum, which the brain interprets as sound.

  • Sound waves are characterized as longitudinal waves that cause particle oscillation parallel to wave motion, resulting in compression and rarefaction zones.

    • Compression Zones: Occur where particles are pressed together.

    • Rarefaction Zones: Occur where particles are stretched apart.

  • Sound travels fastest in solids, slower in liquids, and slowest in gases.

  • Wave Speed Influencers:

    • Bulk Modulus: Indicates resistance to compression; higher bulk modulus increases wave speed.

    • Density: Higher density results in slower sound wave speeds; lower density allows faster propagation.

Doppler Effect

  • Understanding the Doppler Effect includes its formal representation and implications.

  • This phenomenon causes a sonic boom that is experienced on Earth.