NCERT Solutions for Chapter: Waves, Exercise 5: LA

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.

(a) $y=5\cos \left(4x\right)\sin 20t$

Determine the type of wave.

Given below is a function of $x$ and $t$ to represent the displacement of an elastic wave.

 $y=4\sin \left(5x-\frac{t}{2}\right)+3\cos \left(5x-\frac{t}{2}\right)$

State which of the following conditions represent the given equation.
(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.

$y=10 \cos \left[\right(252-250\left)\pi t\right] \cos \left[\right(252+250\left)\pi t\right]$

State which of the following conditions represent the given equation.
(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction

Given below are some functions of $x$ and $t$ to represent the displacement of an elastic wave.

 $y=100\cos (100\pi t+0.5x)$

State which of the following conditions represent the given equation.
(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction

For the harmonic travelling wave $y=2\cos 2\pi (10t-0.0080x+3.5)$ where $x$ and $y$ are in $\mathrm{cm}$ and $\mathrm{t}$ is second. What is the phase difference between the oscillatory motion at two points separated by a distance of

(b) $0.5\mathrm{m}$

For the harmonic traveling wave $y=2\cos 2\pi (10t-0.0080x+3.5)$ where $x$ and $y$ are in $\mathrm{cm}$ and $\mathrm{t}$ is second. What is the phase difference between the oscillatory motion at two points separated by a distance of

(c) $\frac{\lambda }{2}$

For the harmonic travelling wave $y=2\cos 2\pi (10t-0.0080x+3.5)$ where $x$ and $y$ are in $\mathrm{cm}$ and $\mathrm{t}$ is second. What is the phase difference between the oscillatory motion at two points separated by a distance of

(d) $\frac{3\lambda }{4}$ at a given instant of time

For the harmonic travelling wave $y=2\cos 2\pi (10t-0.0080x+3.5)$ where $x$ and $y$ are in $\mathrm{cm}$ and $\mathrm{t}$ is second. 

(e) What is the phase difference between the oscillation of a particle located at $x=100\mathrm{cm},$ at $t$$=\mathrm{T}$ s and $\mathrm{t}=5\mathrm{s}?$