Glossary

Waves carry energy through oscillations in a medium, without the medium itself moving along. The energy of a wave depends on its and , with higher values leading to more energy. This relationship is crucial for understanding wave behavior.

Mathematical expressions describe wave energy, power, and . These formulas help us quantify how waves transport energy and how it changes with distance from the source. Understanding these concepts is key to grasping wave mechanics and their real-world applications.

Energy and Power of Waves

Energy transport in waves

Top images from around the web for Energy transport in waves

  • Sound and Reception | Biology for Majors II View original

    Is this image relevant?

  • Waves | Boundless Physics View original

    Is this image relevant?

  • Sound and Reception | Biology for Majors II View original

    Is this image relevant?

1 of 3

Top images from around the web for Energy transport in waves

  • Sound and Reception | Biology for Majors II View original

    Is this image relevant?

  • Waves | Boundless Physics View original

    Is this image relevant?

  • Sound and Reception | Biology for Majors II View original

    Is this image relevant?

1 of 3
  • Energy in waves is transported through the of the medium (water, air, etc.)
    • The medium itself does not travel with the wave; it simply oscillates about its like a slinky
  • The energy of a wave is directly proportional to the square of its (A2A^2)
    • Doubling the amplitude (height of wave) results in four times the energy
  • The energy of a wave is directly proportional to the square of its frequency (f2f^2)
    • Doubling the frequency (number of waves per second) results in four times the energy
  • The of a wave depends on both its amplitude and frequency
    • A wave with high amplitude (tall) and high frequency (many waves) will have more energy than a wave with low amplitude (short) and low frequency (few waves)

Mathematical expressions for wave energy

  • The (uu) of a wave is the energy per unit volume and is given by:
    • u=12ρv2A2u = \frac{1}{2}\rho v^2 A^2
      • ρ\rho is the density of the medium (how tightly packed the particles are)
      • vv is the (how fast the wave moves through the medium)
      • AA is the amplitude (maximum displacement from equilibrium)
  • The total energy (EE) of a wave can be calculated by multiplying the energy density by the volume (VV) of the wave:
    • E=uVE = uV
  • The power (PP) of a wave is the rate at which energy is transferred and is given by:
    • P=12ρvA2ω2P = \frac{1}{2}\rho v A^2 \omega^2
      • ω\omega is the , related to frequency (ff) by ω=2πf\omega = 2\pi f (converts between cycles/second and radians/second)
  • The intensity (II) of a wave is the power per unit area and is given by:
    • I=PA=12ρvA2ω2I = \frac{P}{A} = \frac{1}{2}\rho v A^2 \omega^2 (power divided by area perpendicular to wave propagation)
  • The describes the mathematical relationship between the wave's displacement, position, and time, connecting these energy concepts to the wave's motion

Wave intensity and propagation

  • Intensity decreases with distance from the source as the wave spreads out (disperses energy over larger area)
    • For a (single origin), intensity follows an : I∝1r2I \propto \frac{1}{r^2}
      • rr is the distance from the source (intensity drops rapidly as you move away)
  • When a wave encounters a surface, it can be reflected (bounces off), absorbed (energy converted to heat), or transmitted (passes through)
    • The intensity of the reflected wave depends on the material properties of the surface (hard surfaces reflect more)
    • The intensity of the transmitted wave is reduced by the amount of energy absorbed or reflected
  • can occur when waves from multiple sources overlap
    • increases the intensity at specific locations (waves in phase, amplitudes add)
    • decreases the intensity at specific locations (waves out of phase, amplitudes cancel)
  • The is used to measure the intensity of sound waves (, each 10 dB is 10x intensity)
    • The level (β\beta) is given by: β=10log⁡II0\beta = 10 \log \frac{I}{I_0}
      • I0I_0 is the reference intensity, typically 10−12 W/m210^{-12} \text{ W/m}^2 for sound waves in air (threshold of human hearing)

Wave Velocities and Standing Waves

  • is the speed at which a specific phase of the wave (e.g., a crest) travels through the medium
  • represents the speed at which the overall shape or envelope of a wave packet moves, often relevant in dispersive media
  • occurs when different frequency components of a wave travel at different speeds in a medium
  • can form when waves are confined to a specific region, such as on a string or in a pipe
    • These stationary wave patterns result from the superposition of incident and reflected waves
  • occurs when the frequency of an applied force matches the natural frequency of a system, leading to large amplitude oscillations in

Key Terms to Review (42)

Absorption: Absorption refers to the process by which a wave's energy is taken up by a medium, resulting in a decrease in the wave's amplitude as it travels through that medium. This process can affect the energy and power of a wave, as the absorbed energy is transformed into other forms, such as heat, rather than continuing to propagate. The efficiency of absorption varies depending on the properties of the medium and the frequency of the wave.
Amplitude: Amplitude is the maximum displacement of a point on a wave from its equilibrium position. It is a measure of the energy carried by the wave.
Amplitude: Amplitude is the maximum displacement or extent of a periodic motion, such as a wave or an oscillation, from its equilibrium position. It represents the magnitude or size of the motion and is a fundamental characteristic of various physical phenomena described in the topics of 1.7 Solving Problems in Physics, 8.4 Potential Energy Diagrams and Stability, 15.1 Simple Harmonic Motion, and beyond.
Angular frequency: Angular frequency, denoted by $\omega$, is the rate of change of angular displacement with time. It is commonly measured in radians per second (rad/s).
Angular Frequency: Angular frequency, often represented by the Greek letter $\omega$ (omega), is a fundamental concept that describes the rate of change of the angular position of an object undergoing rotational or oscillatory motion. It is a crucial parameter in understanding various physical phenomena, including simple harmonic motion, wave propagation, and the behavior of oscillating systems.
Bar graphs of total energy: Bar graphs of total energy visually represent the distribution and conservation of energy in a system. Each bar corresponds to different forms of energy (e.g., kinetic, potential) at specific states or times.
Constructive interference: Constructive interference occurs when two or more waves superimpose to form a resultant wave with a greater amplitude than any of the individual waves. This happens when the phase difference between the waves is an integer multiple of $2\pi$ radians.
Constructive Interference: Constructive interference occurs when two or more waves combine in such a way that their amplitudes add together, resulting in a larger amplitude at the point of intersection. This phenomenon is observed in various wave-based phenomena, including those related to energy and power of waves, interference of waves, standing waves and resonance, normal modes of standing sound waves, and beats.
Decibel: The decibel (dB) is a logarithmic unit used to measure the intensity or power of a sound or other physical quantity. It is commonly used to quantify the relative loudness of sounds and is a fundamental concept in the study of acoustics, sound waves, and sound intensity.
Decibel Scale: The decibel scale is a logarithmic unit used to measure the intensity or power of a wave, particularly in the context of sound and acoustics. It provides a way to quantify and compare the relative levels of different sound intensities or powers.
Decibels: Decibels (dB) are a logarithmic unit used to measure sound intensity levels. They express the ratio of a particular sound intensity to a reference level, usually the threshold of hearing.
Destructive interference: Destructive interference occurs when two waves superimpose to form a resultant wave of lower amplitude. This happens when the crest of one wave aligns with the trough of another, effectively canceling each other out.
Destructive Interference: Destructive interference occurs when two waves interact in such a way that their amplitudes cancel each other out, resulting in a decrease or complete elimination of the wave's intensity at certain points in space. This phenomenon is a fundamental principle in the study of wave behavior and has important applications across various fields, including physics, engineering, and acoustics.
Dispersion: Dispersion is the phenomenon where different components of a wave, such as different frequencies or wavelengths, travel at different velocities through a medium. This causes the wave to spread out and separate into its constituent parts as it propagates.
Energy Density: Energy density is a measure of the amount of energy stored in a given system or material per unit volume or mass. It is an important concept in physics, particularly in the context of energy sources and the propagation of waves.
Energy Transport: Energy transport refers to the movement and transfer of energy, particularly in the context of wave phenomena. It describes how energy is transmitted and propagated through various mediums, enabling the transmission of information, signals, and power.
Equilibrium position: The equilibrium position is the point at which the net force acting on an oscillating system is zero. At this position, the system experiences no acceleration and remains at rest if undisturbed.
Equilibrium Position: The equilibrium position is the point at which a system is in a state of balance, where the net force or torque acting on the system is zero. This concept is fundamental in understanding the behavior of various physical systems, including those related to simple harmonic motion, circular motion, damped oscillations, and wave propagation.
Frequency: Frequency is a fundamental concept in physics that describes the number of occurrences of a repeating event or phenomenon per unit of time. It is a crucial parameter in various areas of physics, including wave behavior, oscillations, and sound propagation.
Group Velocity: Group velocity is the velocity at which the overall shape or envelope of the wave's amplitudes propagates through space. It describes the speed at which the wave packet, or modulation of the wave, travels rather than the speed of the individual wave crests or troughs.
Intensity: Intensity is a measure of the amount of energy or power carried by a wave per unit area perpendicular to the direction of wave propagation. It quantifies the strength or magnitude of a wave and is an important concept in the study of wave energy and power.
Intensity (I): Intensity (I) is the power transferred per unit area where the wave is propagating. It quantifies how much energy a wave delivers to a surface per unit time.
Intensity Equation: The intensity equation quantifies the power per unit area carried by a wave, typically expressed as $$I = \frac{P}{A}$$, where 'I' represents intensity, 'P' is the power of the wave, and 'A' is the area through which the power is distributed. This equation is essential in understanding how energy and power are transmitted through waves, emphasizing the relationship between these variables and the effects on amplitude and distance from the source.
Interference: Interference is the phenomenon that occurs when two or more waves, such as sound or light waves, interact with each other. This interaction can result in the reinforcement or cancellation of the waves, depending on the relative phases of the waves.
Inverse Square Law: The inverse square law is a fundamental principle that describes the relationship between a quantity and the distance from the source of that quantity. It states that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that quantity.
Linear wave equation: The linear wave equation is a second-order partial differential equation that describes the propagation of linear waves, such as sound or light waves, in a medium. It is typically written as $\frac{\partial^2 u}{\partial t^2} = c^2 \nabla^2 u$, where $u$ represents the wave function and $c$ is the speed of the wave.
Logarithmic Scale: A logarithmic scale is a way of measuring and representing quantities that vary over a wide range of values. It is commonly used to display data that spans multiple orders of magnitude, as it allows for the efficient visualization and comparison of such values.
Oscillation: Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. It is commonly seen in mechanical systems like pendulums and springs.
Oscillation: Oscillation refers to the repetitive motion of an object or system back and forth between two or more positions or states. This periodic movement is a fundamental concept that underlies various physical phenomena, including the behavior of potential energy diagrams, the energy dynamics of simple harmonic motion, and the propagation of waves.
Phase Velocity: Phase velocity is the rate at which the phase of a wave propagates in space. It represents the speed at which the wave pattern itself moves, which may be different from the speed at which the individual particles in the medium are oscillating.
Point Source: A point source is a localized and discrete source of a particular substance or form of energy, such as sound or light, that can be approximated as originating from a single point in space. This concept is important in the study of wave phenomena, particularly in the context of energy and power of waves, as well as the understanding of sources of musical sound.
Power Equation: The power equation is a fundamental relationship that describes the power of a wave, which is the rate at which energy is transferred by the wave. This equation is crucial in understanding the energy and power characteristics of various wave phenomena.
Reflection: Reflection is the change in direction of a wave, such as a light or sound wave, when it encounters a boundary or surface. It is the process by which waves are turned back from a surface, causing the wave to change direction and return to the medium from which it originated.
Resonance: Resonance occurs when a system is driven at its natural frequency, leading to a significant increase in amplitude. It is a crucial concept in oscillations and wave phenomena.
Resonance: Resonance is a phenomenon that occurs when a system is driven by a force that matches the system's natural frequency of oscillation, leading to a significant increase in the amplitude of the system's response. This concept is fundamental across various fields in physics, including mechanics, acoustics, and electromagnetism.
Standing waves: Standing waves are wave patterns that result from the interference of two waves traveling in opposite directions, creating nodes and antinodes. These waves appear to be stationary and do not propagate through the medium.
Standing Waves: Standing waves are a pattern of waves formed by the interference of two waves traveling in opposite directions. They are characterized by regions of constructive and destructive interference, resulting in stationary points of maximum and minimum amplitude along the medium.
Total Energy: Total energy is the sum of all forms of energy possessed by an object or system, including kinetic energy, potential energy, and any other forms of energy that may be present. It represents the complete energy state of the system and is a fundamental concept in physics.
Transmission: Transmission refers to the propagation or transfer of a wave or signal from one point to another. It is a fundamental concept in the study of wave phenomena and is crucial in understanding the energy and power characteristics of waves, as well as their interference patterns.
Wave Energy Equation: The wave energy equation is a mathematical expression that describes the relationship between the energy of a wave and its various properties, such as amplitude, wavelength, and frequency. This equation is fundamental in understanding the energy and power associated with wave phenomena in various fields, including physics, engineering, and oceanography.
Wave Equation: The wave equation is a fundamental mathematical equation that describes the propagation of waves, such as sound waves, light waves, and waves on a string. It governs the relationship between the displacement of a wave and the variables that determine its behavior, including time, position, and the properties of the medium through which the wave is traveling.
Wave speed: Wave speed is the distance a wave travels per unit of time. It is usually represented by the symbol $v$ and can be calculated using the formula $v = f \lambda$, where $f$ is the frequency and $\lambda$ is the wavelength.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide