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Relation Between Phase Difference and Path Difference - A Complete Guide
  • Physics
  • Waves
  • relation between phase difference and path difference

Relation Between Phase Difference and Path Difference - A Complete Guide

Vishal kumarUpdated on 02 Jul 2025, 05:07 PM IST

Light is the electromagnetic wave and can travel through the vacuum. Vacuum meaning in Hindi is शून्य स्थान. These electromagnetic waves are categorized based on their wavelength or frequency. Wavelength of any electromagnetic wave is given by λ=c/f, where f is the frequency of the wave. Visible light occupies only a small part of the entire electromagnetic spectrum. Electromagnetic waves with shorter wavelengths and higher frequencies include ultraviolet rays, X-rays, and gamma rays. Long-wavelength, low-frequency electromagnetic waves include infrared, microwave, and broadcast television waves. Interference, in physics, the net effect of the combination of two or more wave trains moving on intersecting or coincident paths. Constructive interference happens when two waves are in phase so that their amplitudes are added to form the wave of more amplitude. Constructive meaning in Hindi is रचनात्मक. Constructive meaning in tamil is ஆக்கபூர்வமான(Ākkapūrvamāṉa)

Relation Between Phase Difference and Path Difference - A Complete Guide
Relation Between Phase Difference and Path Difference

The phase difference is the difference in phase angle of the two waves. Path difference is the difference in path of two waves. The meaning of path in Tamil is பாதை (patai). The relationship between phase difference and path deviation is simple. They are proportional to each other. ∅ is called the phase of the wave. The meaning of phase in English is to adjust something to harmonize it with something else. Phase meaning in physics is related to the angle at which waves travel. Phase difference between two waves ranges from 0 to 2π.

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For any two waves with the same frequency, Phase Difference and Path Difference are related as-

Phase difference formula or path difference formula

Δx= 2×∆∅

Where,

  • Δx is the path difference between the two waves.
  • Phase difference between two waves is represented by ∆∅

Above equation gives the relation between phase difference and path difference.

What is phase difference?

Phase difference can be defined as the variation of angle between any two waves or the particles having the same rate of frequency and starting from the same point. It is calculated in degrees or radians.

What is the path difference?

Path difference is the difference in path of two waves. Path of the wave can be expressed by its wavelength.

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Commonly Asked Questions

Q: What is the formula relating phase difference (φ) to path difference (Δx) and wavelength (λ)?
A:
The formula relating phase difference (φ) to path difference (Δx) and wavelength (λ) is:
Q: How does the medium of wave propagation affect the relationship between phase difference and path difference?
A:
The medium affects this relationship through its impact on the wave's speed and wavelength. In different media, waves may have different speeds and wavelengths for the same frequency. Since the relationship depends on wavelength, changes in the medium can alter the phase difference for a given path difference.
Q: Can phase difference be greater than 360° or 2π radians?
A:
Yes, phase difference can be greater than 360° or 2π radians. However, it's often expressed as an equivalent angle within the range of 0° to 360° (or 0 to 2π radians) by subtracting multiples of 360° (or 2π radians). For example, a phase difference of 450° is equivalent to 90°.
Q: How does frequency affect the relationship between phase difference and path difference?
A:
Frequency itself doesn't directly affect the relationship, but it indirectly influences it through wavelength. Since frequency (f) and wavelength (λ) are related by the wave speed (v) as v = fλ, a change in frequency results in a change in wavelength for a given medium. This, in turn, affects the phase difference for a given path difference.
Q: How does the concept of phase difference and path difference apply to standing waves?
A:
In standing waves, the phase difference between adjacent antinodes is always 180° or π radians. The path difference between these points is always half a wavelength (λ/2). This consistent phase and path difference is what gives standing waves their characteristic node and antinode pattern.

Phase Difference And Path Difference Equation

The relation between the phase difference and phase angle can be given by the following expressions.


FormulaUnit
The relation between phase difference and path differenceΔ∅/∆x= 2No units
Phase DifferenceΔ∅= 2×∆x

Radian or degree
Path DifferenceΔx= 2×∆∅meter

Phase Difference Waves

We define the phase difference of a sine wave as the length of time that one wave precedes or follows another. It should be noted that phase difference is not a property of a single wave, it is a property related to two or more waves.

We call the phase difference “Phase Shift” or “Phase Angle”. We represent the phase transition with the Greek letter Phi denoted ?.

The phase difference can be given by the following sine wave:

sine wave
Figure 1

Also Read:

Interference:

When two waves of equal wavelength intersect, they combine to form one wave. The resulting wave has the same wavelength as the two interacting waves, but its displacement at any point is equal to the algebraic sum of the displacements of the component waves (superposition principle). The formation of the resulting wave is due to the interference of two individual waves. Interference can be destructive or constructive depending on whether the movements are opposite or in the same direction. Structural interference is demonstrated using monochromatic (single wavelength/color) light, if the light waves combine to form waves of greater amplitude than the individual waves. As for light, the resulting wave will be brighter than the two individual waves. In the case of destructive interference, the amplitude of the resulting wave is smaller than the amplitude of the individual waves and will result in weaker light or no light at all (complete destructive interference).These waves are said to have coherence (the property that two waves of the same wavelength will maintain a constant phase relationship). This is why a laser (an instrument that generates intense, parallel beams of coherent light) is an excellent light source for this lab. When light from both slits hits a point on the screen, constructive or destructive interference occurs. As a result, a light or dark band (edge) will appear on the screen. See figure 2.

Interference
Figure 2

When two light waves travel the same distance, they appear on a screen of the same phase and interfere with each other. Waves also interfere with each other (bright fringes) if the difference between the travel distances of each light source is equal to one full wavelength. However, if the difference in the distance the light travels is half a wavelength, then destructive will occur.

Diffraction:

Diffraction: Diffraction refers to the behavior of waves bending around obstacles or passing through small openings. Although light waves have the ability to diffract like other waves, they can be difficult to observe because of their very short wavelength [visible light band: λ (700 nm (red) > > 400 nm (violet)].

Diffraction
Figure 3

The curvature of light as it passes through each of the two slits can be explained by Huygens Principle* (any point on the wavefront can be considered a wave source). Since each slit acts as a point light source, the light wave propagates from the slits and deviates from the line. Diffraction patterns are the result of constructive and destructive interference and therefore look like interference patterns. However, in the case of interference, the slits behave like point light sources, while for diffraction the true width of a single slit is taken into account. The amount of light that will bend is determined by the relative size of the light's wavelength relative to the size of the barrier or slit. If the aperture is much larger than the wavelength of light, the curvature will be nearly undetectable. However, if the size difference is small, the amount of light that will be bent will be small.

Also check-

NCERT Physics Notes:

Commonly Asked Questions

Q: What is the relationship between phase difference and path difference in waves?
A:
Phase difference and path difference are directly related in waves. The phase difference is proportional to the path difference. As the path difference increases, the phase difference also increases. Specifically, a path difference of one wavelength corresponds to a phase difference of 360° or 2π radians.
Q: Why is understanding the relationship between phase difference and path difference important in interference patterns?
A:
Understanding this relationship is crucial for predicting and explaining interference patterns. Constructive interference occurs when waves are in phase (path difference = nλ), while destructive interference occurs when waves are out of phase (path difference = (2n+1)λ/2). This knowledge helps in determining the locations of bright and dark fringes in interference experiments.
Q: How does wavelength affect the relationship between phase difference and path difference?
A:
Wavelength plays a crucial role in the relationship between phase difference and path difference. The phase difference (in radians) is equal to 2π times the path difference divided by the wavelength. This means that for a given path difference, waves with shorter wavelengths will have larger phase differences compared to waves with longer wavelengths.
Q: What is meant by "in-phase" waves, and how does it relate to path difference?
A:
"In-phase" waves are waves that have the same phase at a given point in time and space. This occurs when the path difference between the waves is zero or an integer multiple of the wavelength. In other words, waves are in-phase when their path difference is nλ, where n is an integer and λ is the wavelength.
Q: How can you determine if two waves are completely out of phase?
A:
Two waves are completely out of phase (also known as antiphase) when their phase difference is 180° or π radians. This occurs when the path difference between the waves is an odd multiple of half a wavelength, i.e., (2n+1)λ/2, where n is an integer and λ is the wavelength.

Frequently Asked Questions (FAQs)

Q: What is the importance of the phase difference-path difference relationship in noise reduction in audio systems?
A:
In audio systems, understanding the phase difference-path difference relationship is crucial
Q: How does the phase difference-path difference relationship apply to electron diffraction?
A:
In electron diffraction, the wave nature of electrons leads to interference patterns similar to those seen with light. The path differences between electrons scattered from different atoms in a material lead to phase differences, resulting in a diffraction pattern that provides information about the material's structure.
Q: What is the role of phase difference and path difference in noise reduction headphones?
A:
Active noise reduction headphones use the phase difference-path difference relationship to cancel out unwanted noise. They create sound waves that have a path difference of λ/2 (and thus a phase difference of 180°) compared to the incoming noise, resulting in destructive interference and noise cancellation.
Q: How does the phase difference-path difference relationship apply to radar systems?
A:
In radar systems, the phase difference between transmitted and received signals is used to determine the distance to a target (the path difference). More advanced radar systems can use phase differences between signals received by multiple antennas to determine the direction of a target as well.
Q: What is the significance of a path difference of 2λ (two full wavelengths)?
A:
A path difference of 2λ corresponds to a phase difference of 720° or 4π radians. This is equivalent to a phase difference of 0° or 2π radians, meaning the waves are again in phase. This illustrates the cyclic nature of phase relationships.
Q: How does the phase difference-path difference relationship apply to medical ultrasound imaging?
A:
In ultrasound imaging, the phase differences resulting from different path lengths of reflected sound waves are used to construct images. By precisely measuring these phase differences, the system can determine the depth and location of structures within the body.
Q: Can phase difference be used to measure distance? If so, how?
A:
Yes, phase difference can be used to measure distance. By sending a wave and measuring the phase difference between the transmitted and received signals, the path difference (and thus the distance) can be calculated. This principle is used in phase-shift laser rangefinders and some GPS applications.
Q: What is the role of phase difference and path difference in the operation of lasers?
A:
In lasers, maintaining a specific phase relationship between the light waves is crucial. The cavity length of the laser determines the path difference for a round trip, which must be an integer multiple of the wavelength for constructive interference. This condition, along with population inversion, allows for the amplification of light in the laser.
Q: How does the phase difference-path difference relationship apply to acoustic levitation?
A:
Acoustic levitation uses standing waves to create nodes where objects can be suspended. The phase difference-path difference relationship is crucial in creating these standing waves. By controlling the phase differences between multiple sound sources, stable levitation points can be created and manipulated.
Q: Can phase difference be negative? If so, what does it mean?
A:
Yes, phase difference can be negative. A negative phase difference simply means that one wave lags behind the other. For example, a phase difference of -90° is equivalent to a phase difference of 270° or 3π/2 radians. The sign indicates which wave is leading or lagging.
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