Wave Equation — Prelims Questions

A transverse wave is described by the equation $y(x,t) = 0.02 \sin(0.5x - 4t)$, where $x$ and $y$ are in meters and $t$ is in seconds. What is the wavelength of the wave?

A wave is represented by $y(x,t) = 10 \sin(20t - 4x + \pi/6)$, where $x$ and $y$ are in cm and $t$ is in seconds. What is the speed of the wave?

A wave pulse is described by the equation $y(x,t) = \frac{10}{(x - 2t)^2 + 5}$. What is the speed and direction of propagation of this wave pulse?

Two points on a transverse wave are separated by a distance of $0.75,\text{m}$. If the wavelength of the wave is $3,\text{m}$, what is the phase difference between these two points?

Which of the following functions represents a wave propagating along the positive x-axis?

A sound wave in air has a frequency of $500,\text{Hz}$ and a wavelength of $0.68,\text{m}$. If the wave travels from air into water, where its speed becomes $1500,\text{m/s}$, what will be its new wavelength in water?