A transverse progressive wave on a stretched string has a...

A transverse progressive wave on a stretched string has a velocity of $10 \mathrm{~ms}^{-1}$ and a frequency of $100 \mathrm{~Hz}$. The phase difference between two particles of the string which are $2.5 \mathrm{~cm}$ apart will be (a) $\pi / 8$ (b) $\pi / 4$ (c) $3 \pi / 8$ (d) $\pi / 2$

A transverse progressive wave on a stretched string has a velocity of $10 \mathrm{~ms}^{-1}$ and a frequency of $100 \mathrm{~Hz}$. The phase difference between two particles of the string which are $2.5 \mathrm{~cm}$ apart will be
(a) $\pi / 8$
(b) $\pi / 4$
(c) $3 \pi / 8$
(d) $\pi / 2$

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Key Concepts

Phase Difference

Phase difference measures the shift in phase between two points on a wave separated by a certain distance. It is expressed in radians and calculated using the fraction of the wavelength that the separation distance represents multiplied by 2?, thereby quantifying the relative displacement in the wave's cycle.

Wavelength

Wavelength is the spatial period of the wave, representing the distance between consecutive points in phase, such as crest to crest. It is derived from the relationship between wave velocity and frequency, and it sets the scale for calculating spatial properties like phase differences.

Frequency

Frequency refers to the number of oscillations or cycles that pass a fixed point in a unit time. It is an essential characteristic of any oscillatory motion and directly influences the wave’s energy and wavelength when combined with velocity.

Wave Velocity

Wave velocity defines the speed at which a wave travels through a medium. It is a fundamental concept that links the physical properties of the medium with the wave’s behavior, and it is calculated using the wavelength and frequency of the wave.

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