17.2 Speed of Sound, Frequency, and Wavelength
3 min read•june 18, 2024
Sound waves are fascinating phenomena that shape our auditory world. From the we perceive to the speed at which sound travels, these waves exhibit unique properties that influence how we hear and interact with our environment.
Sound propagation is affected by various factors, including the materials it passes through and temperature. Understanding these influences helps explain why sound behaves differently in diverse settings, from underwater to the atmosphere, and how it changes with temperature fluctuations.
Properties of Sound Waves
Pitch and frequency relationship
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- is the perceived of a sound wave
- Higher frequency waves are perceived as higher pitched sounds (whistling, bird chirps)
- Lower frequency waves are perceived as lower pitched sounds (bass guitar, rumbling thunder)
- The relationship between pitch and frequency is directly proportional
- Doubling the frequency results in a perceived doubling of the pitch (octave)
- Halving the frequency results in a perceived halving of the pitch
- Human hearing range is approximately 20 Hz to 20,000 Hz
- Frequencies below 20 Hz are called (elephants, whales)
- Frequencies above 20,000 Hz are called (bats, medical imaging)
- The loudness of a sound is measured in decibels, which relate to the sound wave's
Speed of sound calculation
- The () is related to its frequency () and () by the equation:
- is the speed of sound in meters per second (m/s)
- is the frequency of the sound wave in Hertz (Hz)
- is the wavelength of the sound wave in meters (m)
- To find the speed of sound, multiply the frequency by the wavelength
- Example: A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. The speed of sound is
- To find the wavelength, divide the speed of sound by the frequency
- Example: A sound wave has a frequency of 1000 Hz and travels at 340 m/s. The wavelength is
Factors Affecting Sound Propagation
Materials and sound propagation
- Sound waves travel at different speeds through different materials
- In general, sound travels faster in solids than in liquids, and faster in liquids than in gases
- Molecules in solids are more closely packed and can transmit vibrations more efficiently
- In general, sound travels faster in solids than in liquids, and faster in liquids than in gases
- The speed of sound in air at 20°C is approximately 343 m/s
- The speed of sound in water at 20°C is approximately 1,482 m/s
- The speed of sound in steel at 20°C is approximately 5,960 m/s
- Sound waves can be reflected, refracted, or absorbed by different materials
- occurs when sound waves bounce off a surface ()
- occurs when sound waves bend as they pass through different materials (underwater communication)
- occurs when sound energy is converted into heat or other forms of energy (soundproofing)
- The through which sound travels affects its propagation characteristics
Temperature effects on sound speed
- The speed of sound in a medium is affected by the temperature of that medium
- In gases, the speed of sound increases with increasing temperature
- Higher temperatures cause gas molecules to move faster, allowing sound waves to propagate more quickly
- The relationship between temperature and speed of sound in air can be approximated by the equation:
- is the speed of sound in meters per second (m/s)
- is the temperature in degrees Celsius (°C)
- In gases, the speed of sound increases with increasing temperature
- For every 1°C increase in temperature, the speed of sound in air increases by approximately 0.6 m/s
- Example: At 0°C, the speed of sound in air is approximately 331.3 m/s. At 20°C, the speed of sound in air is approximately 343.5 m/s.
Sound Wave Characteristics
Longitudinal waves in sound
- Sound waves are , characterized by compressions and rarefactions
- Compressions are areas of high pressure where particles are closer together
- Rarefactions are areas of low pressure where particles are farther apart
- The distance between two consecutive compressions or rarefactions defines the wavelength
Resonance in sound systems
- occurs when an object vibrates at its natural frequency in response to an external force
- This phenomenon can amplify sound waves and is important in musical instruments and acoustic design
Key Terms to Review (23)
Absorption: Absorption is the process by which a substance or energy is taken up and incorporated into a system. This term is particularly relevant in the context of various physical phenomena, including radiation, sound, and light, where absorption plays a crucial role in the behavior and interactions of these forms of energy.
Amplitude: Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium. It plays a crucial role in understanding how energy is transferred in oscillatory systems, impacting the characteristics of waves and sounds.
Beat frequency: Beat frequency is the frequency at which two waves of slightly different frequencies interfere with each other, resulting in a modulation pattern perceived as a periodic variation in amplitude. It is calculated as the absolute difference between the frequencies of the two interfering waves.
Compression: Compression is the process of reducing the volume or size of an object or material by applying force. It involves the application of pressure that causes the particles or molecules within a substance to be pushed closer together, resulting in a decrease in the overall size or dimensions of the object.
De Broglie wavelength: The de Broglie wavelength is the wavelength associated with a particle and is inversely proportional to its momentum. It highlights the wave-particle duality of matter.
Decibel: The decibel (dB) is a logarithmic unit used to measure the intensity or level of various quantities, including sound, electricity, and radio signals. It is a relative measure that compares the magnitude of a quantity to a reference value, often the threshold of human hearing or a standard power level.
Doppler-shifted ultrasound: Doppler-shifted ultrasound is a technique used to measure the change in frequency of sound waves due to the motion of an object, such as blood flow in vessels. It utilizes the Doppler effect to provide information about the speed and direction of moving objects.
Echo: An echo is the reflection of a sound wave that bounces off a surface, creating a delayed and repeated version of the original sound. It is a fundamental concept in the study of the speed of sound, frequency, and wavelength, as the properties of the echo are directly related to these physical quantities.
Frequency: Frequency is a fundamental concept in physics that describes the number of occurrences of a repeating event per unit of time. It is a crucial parameter in various areas of study, including radiation, oscillations, waves, sound, and electromagnetic phenomena.
Infrasound: Infrasound refers to sound waves with frequencies lower than the lower limit of human hearing, typically below 20 Hz. These low-frequency sounds can travel long distances and through various mediums.
Infrasound: Infrasound refers to sound waves with frequencies below the lower limit of human hearing, typically below 20 Hz. These low-frequency sound waves are not audible to the human ear but can be detected and studied using specialized equipment.
Intensity reflection coefficient: The intensity reflection coefficient is a measure of the fraction of incident acoustic wave intensity that is reflected at the boundary between two different media. It is a dimensionless quantity and ranges from 0 to 1.
Longitudinal Waves: Longitudinal waves are a type of wave in which the oscillation of the medium is parallel to the direction of wave propagation. This means the particles in the medium move back and forth in the same direction as the wave is traveling, creating regions of compression and rarefaction.
Medium: A medium, in the context of physics, refers to the material or substance through which a wave or signal propagates. It is the physical environment that supports the transmission of energy or information in the form of waves, such as sound waves or electromagnetic waves.
Pitch: Pitch is the perceived frequency of a sound, determining how high or low it sounds. It is directly related to the frequency of the sound wave.
Pitch: Pitch is the perceived highness or lowness of a sound, determined by the frequency of the sound waves. It is a fundamental characteristic of sound that plays a crucial role in various aspects of acoustics, including sound perception, musical composition, and the Doppler effect.
Rarefaction: Rarefaction is a region in a wave where the medium is less dense compared to the surrounding areas. It is a key concept in understanding the propagation of sound waves and their behavior, particularly in the context of the speed of sound, frequency, wavelength, the Doppler effect, and sonic booms.
Reflection: Reflection is the change in direction of a wave, such as light or sound, when it encounters a boundary or surface. It is a fundamental concept in physics that describes how waves interact with different media and surfaces, leading to various phenomena observed in the physical world.
Refraction: Refraction is the bending of a wave, such as light or sound, when it passes from one medium to another with a different density or refractive index. This phenomenon occurs due to the change in the speed of the wave as it moves between the two mediums, causing it to change direction.
Resonance: Resonance is a phenomenon that occurs when a system is driven by a periodic force at a frequency that matches the system's natural frequency of oscillation, resulting in a significant increase in the amplitude of the system's motion. This concept is fundamental in understanding various physical phenomena, including the behavior of oscillating systems, the propagation of waves, and the operation of electronic circuits.
Speed of Sound: The speed of sound is the distance traveled per unit of time by a sound wave as it propagates through an elastic medium, such as air or water. This fundamental property of sound waves is crucial in understanding various acoustic phenomena, including the Doppler effect and sonic booms.
Ultrasound: Ultrasound is a non-invasive imaging technique that uses high-frequency sound waves to create detailed images of the body's internal structures. It is a versatile tool used in various medical applications, from diagnostic procedures to therapeutic interventions.
Wavelength: Wavelength is a fundamental characteristic of waves, representing the distance between consecutive peaks or troughs in a wave. It is a crucial parameter that describes the spatial extent of a wave and is closely related to other wave properties such as frequency and speed.