A transverse wave of amplitude $5 \mathrm{mm}$ and frequency $10 \mathrm{Hz}$ is produced on a wire stretched to a tension of $100 \mathrm{N}$. If the wave speed is $100 \mathrm{m} {\mathrm{s}}^{-1}$, what average power is the source transmitting to the wire? $({\mathrm{\pi }}^2 = 10)$

A string oscillates according to the equation,
$y^{\text{'}}=\left(0.80 \mathrm{cm}\right)\sin \left[\left(\frac{\mathrm{\pi }}{3} {\mathrm{cm}}^{-1}\right)x\right]\cos \left[\left(40\mathrm{\pi } {\mathrm{s}}^{-1}\right)t\right]$
What is the

$\left(\mathrm{a}\right)$ amplitude

$\left(\mathrm{b}\right)$ speed of the two waves (identical except the direction of travel) whose superposition gives this oscillation?

$\left(\mathrm{c}\right)$ What is the distance between nodes?

$\left(\mathrm{d}\right)$ What is the transverse speed of a particle of the string at the position $x=2.1 \mathrm{cm}$ when $t=0.50 \mathrm{s}$?

The vibration of a string of length $60 \mathrm{cm}$ is represented by the equation,

$y=3 \cos \left(\frac{\pi x}{\text{20}}\right)\cos \left(72\pi t\right)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in $\sec$.

(i) Write down the component waves whose superposition gives the above wave.

(ii) Where are the nodes and antinodes located along the string.

(iii) What is the velocity of the particle of the string at the position $x=5 \mathrm{cm}$ and $t=0.25 \sec$.

The displacement of a wave disturbance propagating in the positive x-direction is given by $y=1/(1+x^2)$ at time $t=0$ and $y=1/[1+(x–1{)}^2]$ at $t=2 \mathrm{s}$ where $x$ and $y$ are in $\mathrm{meters}$. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is:

A transverse wave of amplitude $0.50 \mathrm{m}$, wavelength $1 \mathrm{m}$ and frequency $2 \mathrm{Hz}$ is propagating on a string in the negative $x-$direction. The expression of the wave is