Embibe Experts Solutions for Chapter: Wave Motion on a String, Exercise 1: Exercise - 1

The electric field part of an electromagnetic wave in a medium is represented by $E_{\mathit{x}}=0$; $E_{\mathit{y}}=2.5\frac{\mathrm{N}}{\mathrm{C}}\cos \left[\left(2\pi \times {10}^6\frac{\mathrm{rad}}{\mathrm{m}}\right)t-\left(\pi \times {10}^{-2}\frac{\mathrm{rad}}{\mathrm{s}}\right)x\right]$; $E_2=0.$ The wave is 

If the wavelength of light is $4000 \stackrel{\circ }{\mathrm{A}}$, then the number of waves in $1 \mathrm{mm}$ length will be

In a wave motion $y=a\sin \left(kx-\omega t\right)$, $y$ can represent

Two monochromatic sources of electromagnetic wave $P$ and $Q$ emit waves of wavelength $\lambda =20 \mathrm{m}$ and separated by$5 \mathrm{m}$as shown. $A, B \mathrm{and} C$ are three points where interference of these waves is observed. If phase of a wave generated by $P$ is ahead of wave generated by $Q$ by $\mathrm{\pi }/2$then (given intensity of both waves is $I$) :

$C$ is symmetrical with respect to $P$ and $Q$

As a wave propagates 

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 $t=0.50 \mathrm{s}$?

Two small boats are $10 \mathrm{m}$ apart on a lake. All pop's up and down with a period of $4.0 \mathrm{s}$  due to wave motion on the surface of the water. When one boat is at its highest point, the other boat is at its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is:

Three waves of equal frequency having amplitudes $10 \mu \mathrm{m}$, $4 \mu \mathrm{m}$ and $7 \mu \mathrm{m}$ arrive at a given point with a successive phase difference of $\frac{\mathrm{\pi }}{2}$. The amplitude of the resulting wave in $\mu \mathrm{m}$ is given by