Physics

Problem

A transverse progressive wave travelling on a stretched string is represented by

y(x,t)=0.02\sin\left(4\pi x+200\pi t+\frac{\pi}{6}\right)

where

x

and

y

are in metres and

t

is in seconds. a. (i) Identify the numerical values of amplitude

A

, wave number

k

, angular frequency

\omega

and initial phase

\phi

from the given equation. b. (ii) Calculate the wavelength

\lambda

, frequency

f

and time–period

T

of the wave. c. (iii) State the direction in which the wave propagates and give a brief justification based on the equation. d. (iv) Determine the speed

v

with which the disturbance travels along the string. e. (v) Find the maximum transverse velocity and the maximum transverse acceleration of any particle of the string.

Intuitive explanation

This problem asks you to extract the wave's physical properties from its equation—a skill that hinges on recognizing the standard form $y = A\sin(kx + \omega t + \phi)$ and identifying each parameter's meaning. The key insight is that $k$ (the wave number) and $\omega$ (angular frequency) encode the spatial and temporal structure, while their ratio gives you the wave speed. Once you can read off amplitude, wavelength, period, and direction from the coefficients, you can answer almost any question about this wave's behavior.

Intuitive explanation

Browse the problem library