Name: sound intensity from displacement and pressure
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 5 s
Channel: JoVE

K12 Standards

Alabama Course of Study Science

9-12

Physical Science

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

9-12.PS.2.2.e

Intensity and Pressure of Sound Waves

Consider a sound wave propagating in the x-direction and the displacement of the particles denoted by the wave function y. Recall the expression for a pressure wave.
The particle velocity is given by the time derivative of the displacement, which is obtained.
Recall the expression for power as a product of force and velocity. The power per unit area is given by the product of the force per unit area&#8212;which is the pressure&#8212;and the velocity. The intensity is the time average of this quantity.
Substituting the particle velocity and pressure expressions and taking the average over time, the intensity is derived.
It is further simplified by writing the wave number in terms of the wave velocity, which is related to the bulk modulus.
Recall the relationship between the pressure and displacement amplitudes. Using these three equations, the intensity can be expressed in terms of the pressure amplitude, the density of the medium, and the wave velocity.

intensity and pressure of sound waves

The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The critical step to achieve this is to write the power delivered by the particles on the wave as the product of force and velocity and simplify the force per unit area as the pressure. The velocity of the medium&#39;s particles can be derived from the displacement.
Unlike the time average of a sinusoidal term, which is zero since it is positive and negative for the same amount of time every cycle, the time average of the square of a sinusoidal term is 1/2.
The sound intensity expression in terms of the displacement amplitude is also related to the wave&#39;s frequency. This expression explains why high-frequency waves create the same intensity, even for small amplitude vibrations, compared to low-frequency waves.
The sound intensity expressed via the pressure amplitude does not depend on the wave frequency, making it easier to discuss the intensity&#39;s relationship with the medium&#39;s properties.

The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The ...

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Education

JoVE Core

Physics

Unit 1

Sound

KEY TERMS AND CONCEPTS

sound intensity from displacement and pressure

Sound intensity can be linked to displacement and pressure in a wave. The key idea is to use the wave expressions and the definition of intensity. To do that, the power carried by the particles is written as force times velocity, and the force per unit area is treated as pressure.

The particle velocity can be found from the displacement of the medium. A sinusoidal term averages to zero over time because it is positive and negative for equal parts of each cycle. Its square does not average to zero. The time average of the square of a sinusoidal term is 1/2.

The intensity expression written in terms of displacement amplitude also depends on frequency. That helps explain why a high-frequency wave can produce the same intensity even with a small vibration amplitude as a low-frequency wave. The pressure-amplitude form is different. It does not depend on frequency, so it is easier to use when discussing how intensity relates to the properties of the medium.

Sound Intensity from Displacement and Pressure

sound-intensity-from-displacement-and-pressure

sound waves

How Sound Travels Through Matter

Sound travels through matter as pressure changes in a medium. These changes make the particles of the medium move back and forth around their mean position. Sound can also be modeled as particle displacement as the wave passes through air, water, or another material. In most fluids, sound waves are longitudinal waves. That means the particles vibrate in the same direction that the wave moves. Fluids do not support lateral pressure well, so sound in liquids and gases mainly moves this way. <br...

sound as pressure waves

Sound Pressure in Longitudinal Waves

Sound waves are longitudinal waves that create changing pressure in a medium. Their displacement amplitude can be modeled as a function of position and time. As one column of the medium moves, nearby columns also move. The difference between these successive displacements produces a pressure change compared with the surrounding pressure. This pressure change is called gauge pressure. It varies across the medium because the pressure fluctuation depends on how much one point is displaced...

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perception of sound waves

How Ear Sensitivity Shapes Sound

The human ear does not respond the same way to every sound frequency. Sounds with the same pressure can seem louder or softer when their frequencies change. Ear health also affects this perception, and hearing can decline with age. Regular exposure to loud noises may also damage the ears over time. Pitch depends on both frequency and pressure amplitude, which is the size of the sound wave’s pressure change. Two sounds with the same frequency and pressure amplitude have the same pitch. If the...

speed of sound in solids and liquids

Why Sound Moves Faster in Dense Materials

Sound moves faster in solids and liquids because their particles are close together and can pass along disturbances quickly. Most solids and liquids are incompressible, which means their densities stay nearly constant throughout. When an external force acts on them, the molecules try to return to their original positions. That restoring motion happens because the particles interact with one another. These interactions let sound waves carry information through the material. As a result, sound...

speed of sound in gases

What Changes Sound Speed in Gases?

Sound speed in gases depends on gas properties, pressure, volume, and temperature. Gas molecules move freely, so gases are highly compressible. Because of that compressibility, sound waves travel more slowly through gases than through many other media. The speed of sound in an ideal gas can be found using thermodynamics. Thermodynamics links pressure, volume, and temperature, which helps describe how sound moves through a gas. Newton's laws of motion and the continuity equation from fluid...

deriving the speed of sound in a liquid

Sound Speed in Fluids: Bulk Modulus

Sound speed in fluids depends on a fluid’s bulk modulus and density. These two properties describe how stiff the fluid is and how much inertia it has. For mechanical waves in a fluid, that relationship follows the same pattern used for Young’s modulus and density in solids. The speed of sound in a liquid can be derived by treating the wave as a longitudinal wave moving through the medium. The derivation uses the gauge pressure expression and the impulse-momentum theorem. This same result...

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sound intensity

Measuring How Loud Sound Is

Sound intensity helps describe how loud a sound source is. It depends on how energetically the source vibrates, because those vibrations make the molecules in the medium vibrate as well. Intensity is the energy emitted per unit time per unit area. The area must be perpendicular to the direction the sound wave travels. Using time and area makes the measure reflect the source’s own loudness, even when the source vibrates over a longer time or spreads energy over a larger area. A sound source...

sound intensity level

Measuring Sound with Decibels

Sound intensity level helps measure how loud sound is. The human ear sends sound waves to the brain, and the brain turns those waves into hearing. The loudness of the surrounding environment affects whether a person can tell different sound sources apart. The ear can detect a very wide range of sound intensity. Because of that range, scientists use a logarithmic scale to describe intensity level. Intensity level is a ratio of two intensities, so it has no unit. The standard reference is the...

Sound intensity can be linked to displacement and pressure in a wave. The key idea is to use the wave expressions and the definition of intensity. To do that, the power carried by the particles is written as force times velocity, and the force per unit area is treated as pressure. The particle velocity can be found from the displacement of the medium. A sinusoidal term averages to zero over time because it is positive and negative for equal parts of each cycle. Its square does not average to...

sound waves: interference

Sound Wave Interference in Speakers

Sound wave interference can change the loudness of sound when two waves meet. Sound waves may be modeled as longitudinal waves, where molecules move around an equilibrium position, or as pressure waves. When two identical waves from the same source overlap, their crests or troughs can add together. This is called constructive interference, and it increases amplitude. If identical waves start in phase but travel different path lengths, they can become out of phase. Then a crest can meet a...

interference: path lengths

Interference from Different Path Lengths

Interference from different path lengths explains how two sound sources can create changing patterns in space. The sources may or may not start in phase, but they emit waves at the same frequency. When they are in phase, they are called coherent sources, and that is easy to arrange by feeding both speakers from the same source, such as a tuning fork. These synchronized sources start with the same frequency and the same phase. As the waves move outward, they travel different distances to reach...

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sound waves: resonance

Sound Waves in Tubes and Strings

Sound waves can form resonance patterns in strings and tubes when the boundary conditions match the wave frequency. On a string under tension, symmetrical boundary conditions create a node at each end. A node is a fixed point where the string does not move. Some frequencies then produce standing waves, while other frequencies interfere destructively. Resonance also appears in a hollow tube. In a tube closed at one end and open at the other, a vibrating tuning fork near the open end sends an...

beats

Sound Interference and Beats

Sound interference creates beats when two or more close frequencies combine. In music, this shows up as a changing loudness that rises and falls. The pattern comes from superposition, the adding together of waves. Constructive interference makes the sound stronger, while destructive interference makes it weaker. Music usually contains many changing frequencies from instruments and voices. A single sound at one frequency for a long time can feel dull or even irritating. It can sound like the...

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doppler effect - i

Doppler Shift in Sound and Light

The Doppler effect describes how the frequency of a wave changes when the source and the observer move relative to each other. It was named after the Austrian physicist and mathematician Christian Johann Doppler in 1842. He studied both moving sources and moving observers. A simple example is an ambulance passing a person standing on a street corner. As the ambulance approaches, the siren seems louder. As it moves away, the sound gets quieter. The pitch also changes. The high siren sound...

doppler effect - ii

Doppler Radar and Heart Blood Flow

Doppler effect applications appear in weather forecasting and medical imaging. In these uses, a change in frequency helps show motion. The reflected signal can reveal whether an object is moving toward or away from the source. Meteorologists use Doppler radar to study weather events. A transmitter sends radio waves at a set frequency toward the sky from a weather station. The waves bounce off clouds and precipitation and return to the station. If the reflected radio frequency decreases, the...

shock waves

Sonic Booms and Supersonic Motion

Sonic booms and supersonic motion happen when a sound source moves as fast as, or faster than, sound in the medium. In the Doppler formula for sound, it is usually assumed that sound travels faster than the source. When that assumption fails, a shock wave can form. As the source gets close to the speed of sound, successive wavefronts build up by constructive interference right behind it. Scientists once thought this pressure buildup would keep an airplane from breaking the sound barrier and...

echo

Echo Sound and Distance Detection

Echo is a reflected sound that returns after the original sound has been heard. The human ear cannot tell two sounds apart if they arrive within about 0.1 seconds of each other. When the reflected sound takes longer than that to return, the ear hears two separate sounds instead of one. This effect is easy to notice when the sound source is close to a surface that sends the sound back. If the sound and its reflection are separated by enough time, the result is an echo. A minimum distance of...

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key terms and concepts

See how sound intensity links to displacement and pressure amplitudes, why a squared sine term averages to 1/2, and how frequency changes the result.

Sound Intensity from Displacement and Pressure | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

9-12.P.3.7.b

Texas Essential Knowledge and Skills

High School

PHYS.8

PHYS.8.B

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problem-solving-tuning-of-a-guitar-string

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9-12.PS.2.2.a

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9-12.PS.2.2.b

Sound Waves

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Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As ...

Perception of Sound Waves

The human ear is not equally sensitive to all frequencies in the audible range. It may perceive sound waves with the same pressure but different ...

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Most solids and liquids are incompressible&#8212;their densities remain constant throughout. In the presence of an external force, the molecules tend to ...

Speed of Sound in Gases

The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. ...

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9-12.PS.2.2.c

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The Doppler effect and Doppler shift were named after the Austrian physicist and mathematician Christian Johann Doppler in 1842, who conducted experiments ...

Doppler Effect - II

The Doppler effect has several practical, real-world applications. For instance, meteorologists use Doppler radars to interpret weather events based on ...

d. Use models to illustrate the Doppler effect and explain the changes in sound perception associated with it.

9-12.PS.2.2.d

Standing Waves

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Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. ...

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Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions ...

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Sound Waves: Interference

Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure ...

Interference: Path Lengths

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Two ...

Sound Waves: Resonance

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Standing Electromagnetic Waves

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Standing Waves in a Cavity

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e. Obtain and communicate information from published materials to explain how transmitting and receiving devices use the principles of wave behavior and wave interactions to transmit and capture information and energy. Example: Research and explain how cell phones utilize electromagnetic and mechanical waves.

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Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by ...

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Faraday's Law

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Motional Emf

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Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by ...

3. Construct an explanation of the ways in which modern science uses both magnetic and electric concepts to create usable products. Examples: induction cooktops, stereo speakers, electric motors, wireless chargers

9-12.PS.2.3

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9-12.PS.2.3.a

Sound Intensity from Displacement and Pressure

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