A progressive wave traveling along a medium is described by the equation y = 0.05 \sin(20\… — JAMB UTME

A progressive wave traveling along a medium is described by the equation $y = 0.05 \sin(20\pi t - 4\pi x)$ , where $x$ and $y$ are measured in meters and $t$ is in seconds. What is the speed of the wave in $\text{m/s}$ ?

Answer: 5 m/s

Answer

The speed of the wave is

5.0\text{ m/s}

Comparing

y = 0.05 \sin(20\pi t - 4\pi x)

to the standard wave equation

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

, we find

\omega = 20\pi\text{ rad/s}

and

k = 4\pi\text{ rad/m}

. The wave speed

v

is calculated as

v = \frac{\omega}{k} = \frac{20\pi}{4\pi} = 5.0\text{ m/s}

Step-by-Step Solution

Identify the wave parameters from the standard equation form

\omega = 20\pi\text{ rad/s}

and

k = 4\pi\text{ rad/m}

Matching the given equation

y = 0.05 \sin(20\pi t - 4\pi x)

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

gives the values for angular frequency

\omega

and wave number

k

Compute wave speed using the relationship

v = \frac{\omega}{k}

v = \frac{20\pi}{4\pi} = 5.0\text{ m/s}

Wave speed is defined as the ratio of angular frequency to wave number.

Key Concept

Wave Speed from Wave Equation

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic