(II) A transverse wave on a cord is given by D(x, t)= 0.12...

(II) A transverse wave on a cord is given by $D(x, t)=$ $0.12 \sin (3.0 x-15.0 t),$ where $D$ and $x$ are in $\mathrm{m}$ and $t$ is in s. At $t=0.20 \mathrm{s},$ what are the displacement and velocity of the
point on the cord where $x=0.60 \mathrm{m} ?$

Key Concepts

Instantaneous Displacement

Instantaneous displacement refers to the position of a point on the wave at a specific time and space. It is obtained by substituting the given values of x and t into the wave equation.

Phase of a Wave

The phase in a wave equation, given by the expression inside the sine or cosine function (for instance, kx - ?t), determines the state of oscillation at a particular point in space and time. It embodies the combined effects of spatial position and temporal evolution.

Instantaneous Velocity

Instantaneous velocity in the context of wave motion is the rate of change of displacement with respect to time at a fixed position. This is calculated by taking the partial derivative of the wave equation with respect to time, which provides insight into the dynamic behavior of the wave at any given point.

Transverse Waves

Transverse waves are disturbances that move through a medium such that the motion of the particles is perpendicular to the direction of wave propagation. They are characterized by crests and troughs and can be described using sinusoidal functions.

Wave Equation for a Transverse Wave

The wave equation for a transverse wave expresses displacement as a function of both space and time, typically in the form D(x, t) = A sin(kx - ?t + ?). This form captures the amplitude, spatial variation, time evolution, and phase of the wave.

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