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Relation between Phase Difference and Path Difference is a direct relation as they are directly proportional to each other. Phase difference refers to the difference between phase angles between any two waves. Path difference, on the other hand, refers to the difference in the path traveled by two waves. The relation between phase difference and path difference for any two waves having the same frequency can be expressed as: \(\Delta\chi=\frac{\lambda}{2\pi}\Delta\phi\)
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Key Takeaways: Phase difference, Path difference, Properties of waves, Displacement, Amplitude, Frequency, Waves, Phase angle, Wavelength
Properties of Waves
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Some of the important properties of waves are:
- Displacement: Displacement is the distance traveled by a particle from its mean position. It is measured in meters.
- Amplitude: Amplitude is the maximum displacement of a particle. It is measured in meters.
- Wavelength: The wavelength of the particle is the distance between two adjacent points on the full-wave. It is measured in meters.
- Time Period: The time period refers to the time that is taken by a wave to complete one cycle. It is measured in seconds.
\(Time Period= {1\over frequency}\)
- Frequency: The number of full waves (or a complete cycle) per second is called frequency. It is measured in Hz.
\(Frequency = {1\over timeperiod}\)
Properties of Wave
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Path Difference
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The path difference between any two waves is the difference in the distance they cover. It is the difference in the distance traveled from the source to the observer. The path difference is used to find the interference of waves: constructive and destructive interference.
Phase Difference
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Particles inside waves undergo oscillation. When they move to and fro, the particles go through different phases, from 0° to 360° or zero to 2π. Where π is one period. The particles go through phases, where the particle travels the distance of one wavelength. A particle travels the distance of one wavelength in one period of time. When particles travel in a way that their displacement becomes equal to their wavelength, they go through phases from 0 to 2π.
At any two points in time where the position and motion of the particles are the same, the difference in their phases is known as the phase difference.
Phase Difference
Phase Difference
Particles inside waves undergo oscillation. When they move to and fro, the particles go through different phases, from 0° to 360° or zero to 2π. Where π is one period. The particles go through phases, where the particle travels the distance of one wavelength. A particle travels the distance of one wavelength in one period of time. When particles travel in a way that their displacement becomes equal to their wavelength, they go through phases from 0 to 2π.
At any two points in time where the position and motion of the particles are the same, the difference in their phases is known as the phase difference.
Phase Difference
Relation Between Phase Difference and Path Difference
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Relation between phase difference and path difference for any two waves in motion can be given by:
\(\bigtriangleup x = \frac{\lambda}{2\pi}\bigtriangleup\Phi\)
where x = path difference
\(\Phi\) = phase difference
The SI unit of path difference and the phase difference is the same as they do not have any SI units. The phase difference between any two consecutive points is expressed in terms of radians, whereas the path difference is the integral number of wavelengths in a phase.
Path Difference and Phase Difference
Phase Difference and Path Difference Equation
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The relation between the path difference and the phase difference is given by:
Phase difference (in rad) = 2π (path difference in meters) / λ(wavelength in meter)
Difference Between Phase Difference and Path Difference
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Here are some of the major differences between phase difference and path difference:
| Phase Difference | Path Difference |
|---|---|
| The formula of the phase difference is: (\(\bigtriangleup \Phi = \frac{2\pi\bigtriangleup x}{\lambda}\)) | The formula of path difference is: (\(\bigtriangleup x = \frac{\lambda}{2\pi}\bigtriangleup\Phi\)) |
| The SI unit of phase difference is Radian. | The SI unit of path difference is the meter. |
Things to Remember
- Displacement is measured as the total distance traveled by a particle from its mean position. The unit is meters.
- Amplitude is defined as the maximum displacement of a particle. The unit is meters.
- The wavelength of the particle is defined as the distance between two adjacent points on the full wave. The unit is meters.
- The time period is defined as the time taken by a wave to complete one cycle. The unit is seconds.
- The frequency of a wave is defined as the number of full waves (or a complete cycle) per second. The unit is Hz.
- Phase difference refers to the difference between phase angles between any two waves.
- The SI unit of phase difference is Radian.
- Path difference refers to the difference in the path traveled by two waves.
- The SI unit of path difference is the meter.
- The relation between the phase difference and the path difference for any two waves in motion can be given by: \(\bigtriangleup x = \frac{\lambda}{2\pi}\bigtriangleup\Phi\)
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Previous Year Questions
- When hydrogen atom is in its first excited level, its radius, is….
- When an electron does transition from n=4 to n=2 , then emitted line spectrum will be…...
- α -particle consists of….
- An electron of a stationary hydrogen atom passes from the fifth energy level….
- Complete the equation for the following fission process…. [NEET 1998]
- using non-relativistic approach, the speed of electron in this orbit will be…. [NEET 2015]
- When the glancing angle of incidence of light on a material is...[COMEDK UGET 2004]
- Two waves having intensity ratio 25 : 4 produce interference. The ratio of maximum to...[COMEDK UGET 2004]
- In Young's double slit experiment,1st dark fringe occurs directly...[COMEDK UGET 2009]
- In the diffraction pattern due to a single slit linear width of the central max...[COMEDK UGET 2007]
- In Newton ring experiment, monochromatic light is replaced by white light...[COMEDK UGET 2008]
- In diffraction through a single slit experiment, slit width is halved...[COMEDK UGET 2004]
- When the angle of incidence on a material is\( 60^{\circ}\)…..[KEAM]
- The ratio of the intensities of two waves is 16 : 9. The ratio of their amplitudes is...[KEAM]
- In Young’s double slit experimental setup, if the wavelength alone is...[KEAM]
- A narrow slit of width 2mm is illuminated by monochromatic light of….[KEAM]
- A slit of width a is illuminated by red light of wavelength...[KEAM]
- When the experiment is performed in air with same set up, the angular width of the fringe is...[KEAM]
- In a Fraunhofer diffraction at single slit of width d with incident light of wavelength...[KEAM]
- In Young’s double slit experiment, to increase the fringe width...[KEAM]
Sample Questions
Ques. What is the difference between phase and phase difference? (2 marks)
Ans. Phase: A waveform of the position of a moving particle is known as a “Phase”. It is measured in ‘degrees or Radians’.
Phase difference: The time difference by which a wave leads by or lags to another wave is called “Phase difference” or “Phase angle”. It is defined by '\(\Phi\)'.
Ques. What are the advantages of 3 phases over 1 phase? (2 marks)
Ans. A three-phase circuit gives higher power density than a one-phase circuit at the same ampere, constant wiring size, and lower cost. The three-phase power also makes it easier to balance loads which minimizes harmonic currents and the need for large wires that are neutral in nature.
Ques. What happens when any two given waves have a phase difference of 900? (1 mark)
Ans. For the given two waves, on the left, we have a 90° phase difference and on the right, there is a 180° difference. “90 degrees out of phase” means when one wave is at zero, the other will be at its top point.
Ques. What does 90 degrees out of phase mean? (2 marks)
Ans. Phase is measured in degrees (like angles) and has a relative value. 90 degrees out of phase is bigger out of phase in comparison to 80 degrees, but less than 100 degrees. 180 degrees out of phase is the complete reverse, which is featured by one signal's highest peak correlating with another's most negative peak.
Ques. How do you calculate phase difference? (1 mark)
Ans. The phase difference can be measured on an oscilloscope by determining the time delay between two waveforms along with their period.
Ques. What is phase difference and path difference? (2 marks)
Ans. Phase difference refers to the difference between phase angles between any two waves. Path difference, on the other hand, refers to the difference in the path traveled by two waves.
Ques. Write down any three properties of the wave. (3 marks)
Ans. Some properties of waves are:
- Amplitude: Amplitude is the maximum displacement of a particle. It is measured in meters.
- Wavelength: The wavelength of the particle is the distance between two adjacent points on the full-wave. It is measured in meters.
- Time Period: The time period refers to the time that is taken by a wave to complete one cycle. It is measured in seconds.
Ques. The path difference between two wavefronts emitted by coherent sources of wavelength 5640 A˚ is given by 2.1 microns. What is the phase difference between the wavefronts at that point? (2 marks)
Ans. The phase difference is given by
\(\bigtriangleup \Phi = \frac{2\pi\bigtriangleup x}{\lambda}\)
Therefore,
\(\frac{2\pi*2.1}{0.564} =0.7692\pi\)
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