## Longitudinal Waves – Class 11 | Chapter – 15 | Physics Short Notes Series PDF for NEET & JEE

Longitudinal Waves: Longitudinal waves, also known as compression waves, are waves in which the direction of the oscillation is parallel to the direction of wave propagation. Unlike transverse waves, in which the medium oscillates perpendicular to the direction of wave propagation, in longitudinal waves the medium oscillates back and forth along the same axis as the wave is moving.

Some common examples of longitudinal waves include sound waves in a gas, such as air, and pressure waves in a solid, such as an earthquake wave. In a sound wave, for example, the air molecules oscillate back and forth along the direction of wave propagation, compressing and rarefying the air as the wave moves forward. In an earthquake wave, the solid rock oscillates back and forth along the direction of wave propagation, producing compression and tension in the rock.

Longitudinal waves can be described by several important properties, including wavelength, frequency, velocity, and amplitude. The velocity of a longitudinal wave is determined by the elasticity and density of the medium, and it is usually lower than the velocity of a transverse wave in the same medium. The frequency and wavelength of a longitudinal wave determine its pitch and loudness, respectively.

The reflection and refraction of longitudinal waves can also be important in some physical systems. For example, the reflection and refraction of sound waves are important in the design of acoustics systems, such as concert halls and sound studios, where the sound must be controlled and directed in specific ways.

In conclusion, longitudinal waves play an important role in a variety of physical systems and have a wide range of applications in fields such as sound and vibration engineering, seismology, and medical imaging. Understanding the properties and behavior of longitudinal waves is an important part of physics and engineering.

## Formula of Longitudinal Waves

The formula of a longitudinal wave is:

y(x,t) = y0 cos[ω(t−x/c)]

Where,

• y = Displacement of the point on the traveling sound wave
• x = Distance the point traveled from the wave’s source
• t = Time elapsed
• y0 = Amplitude of the oscillations
• c = Speed of the wave
• ω = Angular frequency of the wave

### Sound Waves

Sound waves are characterized by several important properties, including frequency, wavelength, velocity, and amplitude. The frequency of a sound wave determines its pitch, while the wavelength determines its loudness. The velocity of a sound wave depends on the properties of the fluid medium, such as its temperature, density, and elasticity.

Sound waves can be reflected and refracted as they propagate through a fluid medium, and these effects play a role in many everyday phenomena, such as echoes and the focusing of sound by a parabolic reflector. Sound waves can also interfere with each other, producing standing waves and resonance in systems such as musical instruments and buildings.

In addition to their importance in the production of sound, sound waves play a role in many other areas of science and technology, including medical imaging, where they are used to produce images of the human body, and acoustics, where they are used to control and direct sound in buildings and other structures.

In conclusion, sound waves are an important type of longitudinal wave that play a key role in many physical, biological, and engineering systems. Understanding the properties and behavior of sound waves is an important part of physics, engineering, and the study of acoustics

### Pressure Waves

Pressure waves are a type of longitudinal wave in which the fluid medium oscillates back and forth along the direction of wave propagation, producing changes in pressure. Pressure waves can occur in both solids and liquids, as well as in gases, and they can be produced by a variety of different mechanisms, such as the rapid expansion or compression of a gas, the collision of two solid objects, or the motion of an object through a fluid medium.

In a pressure wave, the fluid medium oscillates back and forth along the direction of wave propagation, creating variations in pressure. The velocity of a pressure wave depends on the properties of the fluid medium, such as its density, temperature, and elasticity, and can be used to study the properties of the medium itself.

Examples of pressure waves include sound waves, seismic waves, and pressure waves in the ocean. In sound waves, for example, the pressure variations in the air produce changes in sound intensity that can be perceived by the human ear. In seismic waves, pressure variations in the Earth’s crust can be used to study the interior structure of the Earth and to monitor earthquakes. In ocean waves, pressure variations can be used to study ocean currents and tides.

In conclusion, pressure waves are a type of longitudinal wave that play a key role in many physical systems, including sound, earthquakes, and the ocean. Understanding the properties and behavior of pressure waves is an important part of physics, engineering, and the study of many natural phenomena.

## Characteristics of Longitudinal Waves

The following are some of the important characteristics of longitudinal waves:

• Direction of oscillation: The direction of oscillation in longitudinal waves is parallel to the direction of wave propagation.
• Particle displacement: In longitudinal waves, the medium oscillates back and forth along the same axis as the wave is moving, causing the particles of the medium to move along the direction of wave propagation.
• Compression and rarefaction: Longitudinal waves are characterized by the presence of regions of high pressure, called compressions, and regions of low pressure, called rarefactions.
• Velocity: The velocity of a longitudinal wave depends on the elasticity and density of the medium and is usually lower than the velocity of a transverse wave in the same medium.
• Wavelength and frequency: The wavelength and frequency of a longitudinal wave determine its pitch and loudness, respectively.
• Reflection and refraction: Longitudinal waves can be reflected and refracted as they propagate through a medium, similar to transverse waves.
• Interference: Longitudinal waves can interfere with each other, producing standing waves and resonance in systems such as musical instruments and buildings.
• Applications: Longitudinal waves play an important role in a variety of physical systems and have a wide range of applications in fields such as sound and vibration engineering, seismology, and medical imaging.

In conclusion, longitudinal waves are a type of wave that are characterized by the direction of oscillation being parallel to the direction of wave propagation, the presence of compressions and rarefactions, and a velocity that depends on the properties of the medium. Understanding the properties and behavior of longitudinal waves is an important part of physics and engineering.

### Examples of Longitudinal Waves

Longitudinal waves are found in a variety of physical systems, and some examples include:

• Sound waves: Sound is a classic example of a longitudinal wave and is produced by the rapid vibration of an object, such as a speaker diaphragm or a musical instrument, which creates pressure variations in a fluid medium.
• Seismic waves: Seismic waves are produced by earthquakes and are used to study the interior structure of the Earth. There are two types of seismic waves: P-waves (primary waves) and S-waves (secondary waves), both of which are longitudinal waves.
• Pressure waves in fluids: Pressure waves can be generated in liquids and gases, such as the pressure waves in the ocean or atmospheric pressure waves.
• Elastic waves: Elastic waves are longitudinal waves that propagate through solids, and they are used in a variety of applications, such as in medical imaging and the study of materials properties.
• Blast waves: Blast waves are produced by explosions and are characterized by high-pressure compressions followed by low-pressure rarefactions.
• Longitudinal waves in plasmas: Plasmas, which are high-temperature ionized gases, can support longitudinal waves, and these waves play an important role in a variety of physical processes, such as in fusion research and space physics.

In conclusion, longitudinal waves are found in a variety of physical systems and have a wide range of applications in fields such as sound and vibration engineering, seismology, medical imaging, and plasma physics. Understanding the properties and behavior of longitudinal waves is an important part of physics and engineering.

## Difference Between Longitudinal Waves and Transverse Waves

Longitudinal Waves Transverse Waves
• These waves move in the direction of their propagation.
• The longitudinal waves are made of refractions and compressions.
• These can be produced in any medium like solid, liquid, or gas.
• Example: Sound Waves
• These waves move in the direction perpendicular to their propagation.
• The transverse waves are made of crests and troughs.
• These can be produced only on solid and liquid surfaces.
• Example: Water Waves

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