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

Transverse Waves: Transverse waves are a type of mechanical wave that involves the oscillation of a medium perpendicular to the direction of wave propagation. In other words, the medium moves up and down, while the wave travels along the surface.

A good example of a transverse wave is a water wave in a pool. When you disturb the surface of the water by throwing a pebble into it, ripples travel away from the point of disturbance, but the water molecules themselves move up and down perpendicular to the direction of the wave.

Another common example of a transverse wave is a light wave. Light is an electromagnetic wave that oscillates perpendicular to the direction of wave propagation, and it is the transverse nature of light that allows us to see objects.

In physics, transverse waves are often described using mathematical models, such as the wave equation, which describe the behavior of the wave as it travels through a medium. These models allow us to understand the properties of transverse waves, such as their speed, wavelength, frequency, and amplitude.

Transverse waves are an important concept in a wide range of fields, including physics, engineering, and technology, and they play a crucial role in many natural phenomena, including the propagation of light, the formation of ocean waves, and the behavior of seismic waves in the Earth’s crust.

## Speed of a Transverse Wave

The speed of a transverse wave is determined by the properties of the medium through which the wave is traveling, as well as the wavelength and frequency of the wave. The relationship between these variables can be described by the wave equation, which gives the speed of a wave (v) as:

v = fλ

where f is the frequency of the wave (measured in Hertz) and λ is the wavelength (measured in meters).

The speed of a transverse wave is determined by the properties of the medium, such as its density, stiffness, and tension. For example, the speed of a transverse wave in a string will be different from the speed of a transverse wave in a metal rod, because the properties of the two materials are different.

In general, transverse waves travel faster in denser and stiffer media, and slower in less dense and more flexible media. The speed of light in a vacuum is an important constant in physics, and is often used as a benchmark to compare the speeds of other types of waves.

Overall, the speed of a transverse wave is an important characteristic that determines how the wave behaves as it travels through a medium, and it is an important concept in a wide range of fields, including physics, engineering, and technology.

## Reflection of Transverse Waves

Reflection of transverse waves occurs when a wave encounters a boundary between two different media, and some or all of the wave energy is reflected back into the original medium. The wave that is reflected will have the same frequency as the incident wave, but its direction and amplitude may be changed, depending on the properties of the boundary and the media.

For example, when a water wave encounters a shoreline, some of the wave energy is reflected back into the water, while the rest continues forward and is absorbed by the shore. This can result in the formation of standing waves, which are waves that remain in one place and do not propagate.

In physics, the reflection of transverse waves is often described mathematically using the principle of wave superposition. This principle states that the total displacement of a wave at a particular point is equal to the sum of the individual displacements of all the waves that are present at that point.

Reflection of transverse waves is an important concept in a wide range of fields, including physics, engineering, and technology. For example, it plays a crucial role in the design of seismographic equipment, which is used to study earthquakes and other seismic phenomena, as well as in the design of underwater acoustics systems, which are used for communication, navigation, and sonar imaging.

## Characteristics of Transverse Waves

Transverse waves are characterized by several key properties, including:

• Amplitude: The amplitude of a transverse wave is the maximum displacement of the medium from its rest position, and it determines the wave’s energy and intensity.
• Wavelength: The wavelength of a transverse wave is the distance between two consecutive crests (or troughs) of the wave, and it determines the wave’s frequency and speed.
• Frequency: The frequency of a transverse wave is the number of complete cycles of the wave that occur in one second, and it determines the wave’s speed and wavelength.
• Speed: The speed of a transverse wave is the distance traveled by the wave in a unit of time, and it is determined by the properties of the medium and the wavelength and frequency of the wave.
• Crest and Trough: A crest is the highest point of a transverse wave, while a trough is the lowest point. The difference between the crest and the trough is the amplitude of the wave.
• Polarization: The polarization of a transverse wave refers to the orientation of the oscillations in the medium with respect to the direction of wave propagation. Transverse waves can be linearly polarized, meaning that the oscillations are in one plane, or elliptically polarized, meaning that the oscillations are in two planes.

These properties of transverse waves are important for understanding the behavior of waves and their interactions with different media. For example, the wavelength of a transverse wave can affect the way that it is refracted (bent) when it passes through a boundary between two different media, while the amplitude of a wave can determine the amount of energy that is transferred as the wave travels through a medium.

## Transverse Waves Formula

There are several important formulas of Transverse Waves. Some of them are:

• Speed = Distance x Time
• Speed of a transverse Wave = Frequency (Hertz) x wavelength (meters)
V (meter per second) = f x λ, [here, c = 3×108 m/sec]
• Frequency = Cycles/Time
• Angular Frequency of a wave ( ω ) = 2 x  x f
Time period (T) – 1/f
• Energy Planck’s constant x frequency, E = h x f, [here, Planck’s constant= 6.626×10-34 J/sec]
• Speed of a wave on a vibrating string: v=
• Speed of light in a different material (V) = Speed of light in a vacuum/ Index of refraction (V= c/n)
Index of refraction differs from medium to medium. For example, the most common index of refraction is of water, 1.3.
• Constructive inference d sin θ = mλ
for m = 0,1,-1,2,-2
• Destructive inference = d sin θ = (m+0.5)λ for m = 0,1,-1,2,-2

## Examples of Transverse Waves

Transverse waves are found in a variety of different physical systems, and can take many different forms. Here are some common examples of transverse waves:

• Light Waves: Light waves are a type of transverse wave that travel through a vacuum at the speed of light, and they are responsible for the phenomenon of vision. Light waves can be polarized, meaning that the oscillations are in a single plane, and they can be described by their frequency, wavelength, and amplitude.
• Electromagnetic Waves: Electromagnetic waves are a type of transverse wave that include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Electromagnetic waves are responsible for a wide range of phenomena, including communication, navigation, and imaging.
• Surface Waves: Surface waves are a type of transverse wave that travel along the surface of a fluid, such as water or air. Examples of surface waves include ocean waves, wind-generated waves, and tsunamis.
• Radio Waves: Radio waves are a type of transverse electromagnetic wave that are used for communication, such as in radio and television broadcasting, as well as in wireless communication technologies like cell phones and Wi-Fi.
• Mechanical Waves: Mechanical waves are a type of transverse wave that involve the displacement of a physical medium, such as a string or a rod. Examples of mechanical waves include waves in a plucked guitar string, waves in a suspension bridge, and waves in a tightrope walker’s rope.

These are just a few examples of the many different types of transverse waves that exist in the natural world. Understanding the properties of transverse waves and their interactions with different media is an important part of physics and engineering, and has a wide range of applications in fields such as communication, navigation, and energy.

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