## Amplitude and Phase – Class 11 | Chapter – 15 | Physics Short Notes Series PDF for NEET & JEE

Amplitude and Phase: Amplitude and phase are two important properties of waves that describe different aspects of the wave’s behavior. Amplitude measures the strength or intensity of a wave, phase measures its position relative to a reference wave. Both amplitude and phase are important properties of waves that can affect their behavior and how they interact with other waves.

### What is Amplitude?

Amplitude is a measure of the maximum displacement or disturbance of a wave from its rest or equilibrium position. In other words, it is the height or size of the wave. The amplitude of a wave determines its strength and energy, and it is directly proportional to the intensity of the wave. The amplitude can be expressed in terms of displacement, velocity, or pressure, depending on the type of wave being considered.

For example, in a transverse wave, the amplitude is the maximum height of the crest or the depth of the trough of the wave, measured from the equilibrium position. In a longitudinal wave, the amplitude is the maximum compression or rarefaction of the medium, measured from its average or rest density.

The amplitude of a wave is a key characteristic that determines its behavior and interactions with other waves and with its surroundings. For example, when two waves with the same frequency but different amplitudes interfere, the resulting wave will have an amplitude that is equal to the sum of the individual amplitudes. The amplitude also affects the energy carried by the wave and the ability of the wave to do work, as well as its ability to be detected and measured.

In conclusion, the amplitude of a wave is a measure of its maximum displacement or disturbance and is a key characteristic that determines its behavior and interactions with its surroundings.

### Amplitude Formula

The highest displacement of the waves is referred to as amplitude. The amplitude formula helps in the calculation of the sine and cosine functions. A is the symbol for amplitude. The sine (or cosine) function can be written as:

= A sin (ωt + θ) or = A cos (ωt + θ)

OR

Position = amplitude × sine function (angular frequency × time + phase difference)

Here,

• x = displacement of wave (meter)
• A = amplitude
• ω = angular frequency (rad/s)
• t = time period
• θ = phase angle

The amplitude formula can alternatively be written as the average of the sine or cosine function’s highest and lowest values. The absolute value of the amplitude is always used (Amplitude = (max + min) / 2)

### Types of Amplitude

There are two types of amplitude in waves: peak amplitude and root-mean-square (RMS) amplitude.

• Peak amplitude: The peak amplitude is the maximum height or size of a wave, measured from its rest or equilibrium position to the crest or the trough of the wave. It is the most commonly used definition of amplitude, especially in the field of optics and in the study of transverse waves.
• Root-mean-square (RMS) amplitude: The root-mean-square (RMS) amplitude is defined as the square root of the mean of the squares of the wave’s values. It is used in the study of longitudinal waves and in electrical engineering, where it is a measure of the effective voltage or current of a waveform. The RMS amplitude is proportional to the square root of the power of the wave, and it is often used as a more meaningful measure of amplitude in these fields.

In conclusion, the two types of amplitude in waves are peak amplitude and root-mean-square (RMS) amplitude, which are used to describe the height or size of a wave in different ways. The peak amplitude is the maximum height of the wave, while the RMS amplitude is a measure of the effective voltage or current of a waveform and is proportional to the square root of the power of the wave.

### What is  Phase ?

Phase is a concept used to describe the relative timing of two or more waves. It refers to the position of a wave relative to a reference point in time, and it is expressed in degrees or radians. The phase of a wave determines the timing of its peaks, troughs, and zero crossings with respect to other waves or with respect to a reference wave.

The phase difference between two waves is the difference in the timing of their peaks or zero crossings, and it is a measure of the relative phase of the waves. The phase difference can be positive, negative, or zero, depending on whether the waves are in phase, out of phase, or perfectly in phase with each other, respectively.

The phase of a wave also determines its behavior in interference and superposition, as well as its behavior when it is reflected, refracted, or transmitted through different media. For example, when two waves with the same frequency and amplitude interfere, the resulting wave will have a different amplitude and phase depending on the phase difference between the two waves.

In conclusion, phase is a measure of the relative timing of two or more waves and determines the position of a wave relative to a reference point in time. It plays a crucial role in the behavior of waves in interference, superposition, and other wave phenomena, and it is expressed in degrees or radians.

### Types of phase

There are two types of phase in waves: phase angle and phase shift.

• Phase angle: The phase angle is the measure of the relative phase of two waves in terms of an angle, expressed in radians or degrees. It is the difference in the timing of the peaks or zero crossings of the two waves, and it can be positive, negative, or zero, depending on whether the waves are in phase, out of phase, or perfectly in phase with each other, respectively. The phase angle determines the relative phase of the waves and the resulting wave shape when they interfere.
• Phase shift: The phase shift is the difference in the phase of a wave at different points in space or time. It is a measure of the spatial or temporal shift of a wave with respect to a reference wave, and it is expressed in radians or degrees. The phase shift can be caused by a variety of factors, such as reflection, refraction, diffraction, or the passage of the wave through a medium with varying properties.

In conclusion, there are two types of phase in waves: phase angle and phase shift. The phase angle is the measure of the relative phase of two waves in terms of an angle, while the phase shift is the difference in the phase of a wave at different points in space or time. These two concepts play a crucial role in the understanding of wave behavior and wave interactions.

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