Name: sound waves in tubes and strings
Uploaded: 2023-04-30T11:11:43.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Physical Science

Waves and Electromagnetic Radiation

3.2.9-12.V

Sound Waves: Resonance

Resonance is a special case of forced oscillation in a system, wherein the first object&#39;s driving frequency matches the second object&#39;s natural frequency, forcing the second object to vibrate at the same frequency with a significantly higher amplitude.
Consider a tuning fork and a hollow cylindrical tube closed at one end. When the tines of the tuning fork vibrate at their natural frequency, a sound wave is generated, which impinges upon the entrance of the tube, forcing the air inside the tube to vibrate at the same frequency. If the tuning fork&#39;s natural frequency matches the air column&#39;s normal modes, resonance results in a louder sound.
A similar thing happens for a tube open at both ends. The air columns in the tube have maximum air displacements at both ends, and thus, the reflections of the sound at each end produce a large-amplitude wave for particular frequencies.
The resonant frequencies for a tube open at both ends follow the same equation as that of a standing wave on a string fixed at both ends.

sound waves: resonance

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound waves that resonate depend on the boundary conditions.
For instance, consider a tube that is closed at one end and open at the other. If a vibrating tuning fork is placed near the open end of the tube, an incident sound wave travels through the tube and reflects off the closed end. The reflected sound has the same frequency and wavelength as the incident sound wave but travels in the opposite direction. At the closed end of the tube, the air molecules have very little freedom to oscillate, and a node arises. At the open end, the molecules are free to move, and at the right frequency, an antinode occurs.
Unlike the symmetrical boundary conditions for standing waves on a string, the boundary conditions for a tube open at one end and closed at the other end are anti-symmetrical; there is a node at the closed end and an antinode at the open end. If the tuning fork has the right frequency, the air column in the tube resonates loudly. Thus, it vibrates very little at most frequencies, suggesting that the air column has only specific natural frequencies.
In another instance, if the standing waves travel through a tube that is open at both ends, the boundary conditions are symmetrical&#8212;an antinode at each end. The resonance in tubes open at both ends can be analyzed similarly to those for tubes closed at one end. The air columns in tubes open at both ends have maximum air displacements at both ends.
This text is adapted from <a href="https://openstax.org/books/university-physics-volume-1/pages/17-4-normal-modes-of-a-standing-sound-wave">Openstax, University Physics Volume 1, Section 17.4: Normal Modes of a Standing Sound Wave. </a>

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical ...

Education

JoVE Core

Physics

Unit 1

Sound

KEY TERMS AND CONCEPTS

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 incident sound wave through the tube. The wave reflects from the closed end and returns with the same frequency and wavelength, but it travels in the opposite direction. The closed end acts as a node because the air molecules have very little freedom to oscillate.

The open end of that tube acts differently. The air molecules are free to move there, and at the right frequency, an antinode forms. An antinode is a point of maximum motion. These anti-symmetrical boundary conditions give the tube only specific natural frequencies, so it resonates loudly at some frequencies and vibrates very little at most others.

A tube open at both ends has symmetrical boundary conditions again, but this time there is an antinode at each end. The air columns in these tubes can be analyzed in a similar way to tubes closed at one end. In both cases, the boundary conditions decide which sound frequencies resonate and which do not. At the ends of an open-at-both-ends tube, the air displacement is maximum.

Sound Waves in Tubes and Strings

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...

intensity and pressure of sound waves

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...

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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 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

Explore how boundary conditions create resonance in strings and sound tubes, including nodes, antinodes, and standing waves in open and closed tubes.

Sound Waves in Tubes and Strings | 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.

Louisiana Student Standards for Science

High School

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

Waves And Their Applications In Technologies For Information Transfer

HS-PS4-1

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Energy And Waves

Waves

Wave properties

Tennessee Academic Standards

Waves and Their Applications in Technologies for Information Transfer

PHYS.PS4.4

Virginia  Standards of Learning

HIgh School

PS.6

PS.6.c

PH.5

PH.5.b

Alabama Course of Study Science

9-12.PS.2.2.e

9-12.P.3.7.b

Next Generation Science Standards

HS-PS4-3

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-3.

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Sound Waves in Tubes and Strings

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