A progressive wave traveling through a uniform medium is described by the displacement equ… — JAMB UTME

A progressive wave traveling through a uniform medium is described by the displacement equation $y = 0.04 \sin\left(150\pi t - 6\pi x\right)$ , where $x$ and $y$ are measured in meters and $t$ is in seconds. What is the speed of propagation of the wave?

Answer: 25 m/s

Answer

The speed of propagation of the wave is 25 m/s.

By matching

y = 0.04 \sin(150\pi t - 6\pi x)

to the standard wave equation

y = A \sin(\omega t - kx)

, we obtain

\omega = 150\pi\text{ rad/s}

and

k = 6\pi\text{ rad/m}

. The speed of the wave

v

is calculated as

v = \frac{\omega}{k} = \frac{150\pi}{6\pi} = 25\text{ m/s}

Step-by-Step Solution

Compare the given wave equation with the general progressive wave equation

y = A \sin(\omega t - kx)

Angular frequency

\omega = 150\pi\text{ rad/s}

and wave number

k = 6\pi\text{ rad/m}

Matching coefficients allows direct extraction of angular frequency and spatial wave number.

Calculate the wave speed using the relationship

v = \frac{\omega}{k}

v = \frac{150\pi}{6\pi} = 25\text{ m/s}

The velocity of a progressive wave is equal to the ratio of its angular frequency to its wave number.

Key Concept

Determining wave velocity from progressive wave equation parameters

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