17.2 Speed of Sound
3 min read•june 24, 2024
Sound waves are fascinating vibrations that travel through various mediums. They have key properties like , , and speed, which are interconnected by the equation v = fλ. Understanding these basics helps us grasp how sound behaves in different situations.
The varies depending on the medium and conditions. In gases, it's affected by temperature, while in liquids and solids, and play crucial roles. These factors influence how sound travels in our everyday world.
Properties of Sound Waves
Wavelength, frequency and sound speed
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- Speed of sound () is the product of () and () expressed by the equation
- Frequency is the number of wave cycles passing a fixed point per unit time measured in (Hz), the number of cycles per second
- Wavelength is the distance between two consecutive in-phase points on a wave measured in meters (m) or other length units
- For a given sound speed, as frequency increases, wavelength decreases and vice versa ()
Speed of sound calculations
- Sound speed in a medium depends on the medium's properties, generally traveling faster in solids than liquids, and faster in liquids than gases
- In gases, sound speed depends on temperature, for ideal gases, sound speed () is given by
- is the (ratio of specific heats)
- is the (8.314 J/mol·K)
- is the absolute temperature in Kelvin (K)
- is the gas (kg/mol)
- At 20℃ (293.15 K), sound speed in air is approximately 343 m/s
- In liquids and solids, sound speed depends on the material's () and density () given by the equation
Factors Affecting the Speed of Sound
Factors affecting sound speed
- Temperature: In gases, higher temperatures lead to faster sound speed due to increased gas molecule motion and faster sound wave propagation
- Density: Sound generally travels faster in less dense materials (sound travels faster in air than water, which is denser than air)
- Elasticity (): Materials with higher elasticity (higher bulk modulus) allow faster sound travel due to more efficient vibration transfer between molecules
- (in gases): Humidity has a minor effect on sound speed in air, slightly increasing with humidity due to water vapor's lower density compared to dry air
- : The specific characteristics of the medium, such as its , significantly influence sound propagation
Applications of sound speed equation
- Calculating distance to a lightning strike
- Measure time delay between seeing lightning and hearing thunder
- Multiply time delay by sound speed in air to determine distance (5 s delay and 343 m/s sound speed gives a distance of )
- Determining ocean depth using
- Measure time for sound wave to travel from ship to ocean floor and back
- Multiply half the time delay by sound speed in water (approximately 1,500 m/s) to calculate depth
- Designing concert halls and auditoriums considering sound speed in air and room dimensions to create optimal sound quality, as sound speed affects and acoustic properties
Sound Wave Characteristics
- Sound waves are , where particles of the medium oscillate parallel to the direction of wave propagation
- These waves consist of alternating regions of compression (high pressure) and rarefaction (low pressure)
- in a medium create that propagate through the material
- The speed and behavior of sound waves depend on the properties of the medium through which they travel
Key Terms to Review (30)
Acoustic Impedance: Acoustic impedance is a measure of the opposition to the flow of sound energy through a medium, such as air or a solid material. It is a crucial concept in the understanding of the propagation and behavior of sound waves.
Adiabatic index: The adiabatic index, often denoted as $$ ext{k}$$ or $$ ext{γ}$$ (gamma), is the ratio of the specific heat capacities of a gas at constant pressure ($$C_p$$) to that at constant volume ($$C_v$$). This dimensionless number plays a crucial role in thermodynamics and fluid dynamics, especially in understanding how sound waves propagate through different mediums. In contexts involving the speed of sound, it helps determine how the properties of gases influence the transmission of sound and energy transfer within those gases.
Bulk modulus: Bulk modulus is a measure of a material's resistance to uniform compression. It is defined as the ratio of pressure increase to the resulting relative decrease in volume.
Bulk Modulus: Bulk modulus is a measure of a material's resistance to uniform compression. It quantifies how much a material's volume decreases when subjected to a given increase in pressure, and is an important parameter in understanding the behavior of solids, liquids, and gases under compression.
Compression Waves: Compression waves, also known as longitudinal waves, are a type of mechanical wave where the displacement of the medium is parallel to the direction of wave propagation. These waves involve the compression and rarefaction of the medium, causing the particles to oscillate back and forth along the direction of the wave.
Density: Density is a fundamental physical property that describes the mass per unit volume of a substance. It is a measure of how much matter is packed into a given space and is a crucial concept in understanding the behavior of fluids, solids, and gases across various physics topics.
Elastic property: Elastic property refers to the ability of a material to return to its original shape after being deformed by an external force. It is crucial in determining how sound waves propagate through different media.
Elasticity: Elasticity is a material property that describes the ability of a substance to deform under stress and then return to its original shape and size when the stress is removed. It is a fundamental concept in physics and engineering that governs the behavior of materials under various loading conditions.
Frequency: Frequency is the number of oscillations or cycles that occur in a unit of time, typically measured in Hertz (Hz). It represents how often a repeating event such as a sound wave occurs per second.
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.
Hertz: Hertz (Hz) is the unit of frequency, which measures the number of cycles or oscillations that occur per second. It is a fundamental concept in physics, particularly in the study of wave phenomena, such as sound waves and electromagnetic waves.
Humidity: Humidity refers to the amount of water vapor present in the air. It is an important factor that affects the speed of sound, as the presence of water molecules in the air can influence the propagation of sound waves.
Inertial property: Inertial property is a characteristic of matter that quantifies its resistance to changes in motion. In the context of sound, it often refers to the mass density of a medium.
Inverse Relationship: An inverse relationship is a mathematical relationship between two variables where an increase in one variable corresponds to a decrease in the other variable, and vice versa. This type of relationship is often represented by a negative correlation or a downward-sloping line on a graph.
Linear mass density: Linear mass density is the measure of mass per unit length of a one-dimensional object, such as a string or rod. It is typically denoted by the symbol $\lambda$ and expressed in units of kg/m.
Longitudinal Waves: Longitudinal waves are a type of wave in which the displacement of the medium is parallel to the direction of wave propagation. This means the particles in the medium oscillate back and forth in the same direction as the wave is traveling.
Medium Properties: Medium properties refer to the physical characteristics of a material through which sound waves travel, influencing the speed and behavior of sound. These properties, including density, elasticity, and temperature, play crucial roles in determining how sound propagates within different media, such as gases, liquids, and solids.
Molar Mass: Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is a fundamental property that describes the relationship between the mass of a substance and the number of particles (atoms, molecules, or ions) it contains.
Newton-Laplace Equation: The Newton-Laplace equation is a fundamental relationship that describes the speed of sound propagation in a medium. It establishes a connection between the properties of the medium, such as its density and compressibility, and the velocity at which sound waves travel through it.
Pressure Variations: Pressure variations refer to the changes in the pressure of a medium, such as air or a fluid, over time or space. These variations can have significant impacts on the behavior and properties of the medium, particularly in the context of the speed of sound.
Reverberation Time: Reverberation time is the time required for the sound pressure level in an enclosed space to decrease by 60 decibels (dB) after the sound source has been turned off. It is a critical parameter in the design and analysis of acoustic environments, as it directly affects the quality of sound and speech intelligibility in a room.
Seismic waves: Seismic waves are waves of energy that travel through the Earth's layers as a result of an earthquake, volcanic eruption, or other subterranean explosion. These waves can be classified into different types based on their propagation characteristics and speed.
Sonar: Sonar is a technique that uses sound waves to detect and locate objects underwater. It is an acronym for Sound Navigation and Ranging, and it works by transmitting sound waves and analyzing the reflected echoes to determine the distance, direction, and characteristics of submerged objects.
Speed of Sound: The speed of sound is the distance traveled by a sound wave per unit of time. It is the rate at which sound waves propagate through a medium, such as air, water, or a solid material. The speed of sound is an important concept in the study of sound waves and their behavior.
Tweeter: A tweeter is a type of loudspeaker designed to reproduce high-frequency sounds, typically from around 2 kHz to 20 kHz. It is crucial in sound systems for delivering clear and accurate high-pitched audio.
Universal Gas Constant: The universal gas constant, often denoted as R, is a fundamental physical constant that relates the pressure, volume, amount of substance, and absolute temperature of a gas. It is a crucial parameter in the study of gas behavior and thermodynamics.
Wavelength: Wavelength is the distance between successive crests or troughs of a wave. It is typically represented by the Greek letter lambda ($\lambda$).
Wavelength: Wavelength is a fundamental characteristic of waves, representing the distance between consecutive peaks or troughs of a wave. It is a crucial parameter that describes the spatial properties of various wave phenomena, including light, sound, and other types of oscillations.
Woofer: A woofer is a type of loudspeaker designed to reproduce low-frequency sounds, typically in the range of 20 Hz to 2 kHz. It is commonly used in audio systems to handle bass and sub-bass frequencies.
Young’s modulus: Young's modulus, also known as the elastic modulus, is a measure of the stiffness of a solid material. It quantifies the relationship between tensile stress and strain in a material.