If the equation for a transverse wave is y=A Sin 2 π{(1 / T)-(x / λ)}. then for what wavelength

step 1 Hello and welcome to this video solution of numerate. So here we are given that if the equation

If the equation for a transverse wave is y=A Sin 2 π{(1 /...

If the equation for a transverse wave is $\mathrm{y}=\mathrm{A} \operatorname{Sin} 2 \pi$ $\{(1 / \mathrm{T})-(\mathrm{x} / \lambda)\}$. then for what wavelength will the maximum velocity of the particle be double the wave velocity ? (A) $(\pi \mathrm{A} / 4)$ (B) $(\pi \mathrm{A} / 2)$ (C) $\pi \mathrm{A}$ (D) $2 \pi \mathrm{A}$

If the equation for a transverse wave is $\mathrm{y}=\mathrm{A} \operatorname{Sin} 2 \pi$ $\{(1 / \mathrm{T})-(\mathrm{x} / \lambda)\}$. then for what wavelength will the maximum velocity of the particle be double the wave velocity ?
(A) $(\pi \mathrm{A} / 4)$
(B) $(\pi \mathrm{A} / 2)$
(C) $\pi \mathrm{A}$
(D) $2 \pi \mathrm{A}$

Key Concepts

Transverse Waves

Transverse waves are disturbances in which the displacement of the medium is perpendicular to the direction of wave propagation. This concept is fundamental in understanding how energy is transmitted through oscillatory motion in various physical systems.

Wave Equation

The wave equation is a mathematical expression that describes the displacement of a wave as a function of both space and time. Its sinusoidal form, typical for many physical waves, encodes parameters like amplitude, wavelength, and period, which are essential for analyzing wave behavior.

Particle Velocity

In wave motion, particle velocity refers to the speed at which a point in the medium oscillates due to the presence of the wave. It is derived as the time derivative of the displacement function and generally varies sinusoidally, with its maximum value being proportional to both the amplitude and the angular frequency.

Wave Propagation Speed

The wave propagation speed is the rate at which the overall wave shape or disturbance travels through the medium. It is determined by the relationship between wavelength and period (or frequency) and is distinct from the oscillatory speed of individual particles in the medium.

Angular Frequency

Angular frequency is a measure of how rapidly a periodic function completes a cycle, typically defined as 2? divided by the period. It provides a link between time-domain oscillations and their corresponding sinusoidal representations in wave equations.

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