The transverse displacement y (x, t) of a wave on a string is given by yleft( {x,t} right) = {e^{

Q: The transverse displacement $y (x, t)$ of a wave on a string is given by $y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \;xt} \right)}}$ .This represents a

b Given wave equation is $y(x, t)=e^{\left(-a x^{2}+b t^{2}+2 \sqrt{a b} x t\right)}$ $=e^{-\left[(\sqrt{a x})^{2}+(\sqrt{b} t)^{2}+2 \sqrt{a} x \cdot (\sqrt{b} t)\right]}=e^{-(\sqrt{a x}+(\sqrt{b} t)^{2}}$ $=e^{-(x+\sqrt{\frac{b}{a}} t)^{2}}$ It is a function of type $y=f(x+v t)$ $\Rightarrow$ Speed of wave $=\sqrt{\frac{b}{a}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

The transverse displacement $y (x, t)$ of a wave on a string is given by $y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \;xt} \right)}}$ .This represents a

Awave moving in $+ x$ direction speed $\sqrt {\frac{a}{b}} $
Bwave moving in $-x$ direction with speed $\sqrt {\frac{b}{a}} $
Cstanding wave of frequency $\sqrt b $
Dstanding wave of frequency $\frac{1}{{\sqrt b }}$

AIEEE 2011, Diffcult

STD 11 Science
NEET
STD 11 - 14. waves and sound
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27\,^o C$ two successive resonances are produced at $20\, cm$ and $73\, cm$ of column length. If the frequency of the tuning fork is $320\, Hz,$ the velocity of sound in air at $27\,^o C$ is .... $m/s$
View Solution
2
If the density of oxygen is $16$ times that of hydrogen, what will be the ratio of their corresponding velocities of sound waves
View Solution
3
A sound wave of frequency $245 \,Hz$ travels with the speed of $300\, ms ^{-1}$ along the positive $x$-axis. Each point of the wave moves to and fro through a total distance of $6 \,cm$. What will be the mathematical expression of this travelling wave ?
View Solution
4
The displacement of a particle in string stretched in $X$ direction is represented by $y.$ Among the following expressions for $y,$ those describing wave motions are
View Solution
5
Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\,\, Hz.$ The fractional increase in the tension of one of the wires which will lead to occurrence of $6\,\, beats/s$ when both the wires oscillate together would be
View Solution
6
Standing waves can be produced
View Solution
7
If wavelength of a wave is $\lambda = 6000Å.$ Then wave number will be
View Solution
8
Doppler effect is applicable for
View Solution
9
The equation of a wave on a string of linear mass density $0.04\, kgm^{-1}$ is given by : $y = 0.02\,\left( m \right)\,\sin \,\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} - \frac{x}{{0.50\left( m \right)}}} \right)} \right]$. The tension in the string is ..... $N$
View Solution
10
A wave travels in a medium according to the equation of displacement given by $y(x,\,t) = 0.03\sin \pi (2t - 0.01x)$ where $y$ and $x$ are in metres and $t$ in seconds. The wavelength of the wave is .... $m$
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free