The disturbance $y (x, t)$ of a wave propagating in the positive. $x-$ direction is given by $y = \frac{1}{{1 + {x^2}}}$ at time $t\,= 0$ and by $y = \frac{1}{{\left[ {1 + {{\left( {x - 1} \right)}^2}} \right]}}$ at $t\, = 2\, s$, where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in $m/s$ is
AIEEE 2012, Diffcult
Download our app for free and get started
The equation of wave at any time is
obtained by putting $X=x-vt$
$y=\frac{1}{1+x^{2}}=\frac{1}{1+(x-v t)^{2}}$ $...(i)$
We know at $t=2 \mathrm{sec}$
$y=\frac{1}{1+(x-1)^{2}}$ $...(ii)$
On comparing$ (i)$ and $(ii)$ we get
$v t=1$
$V=\frac{1}{t}$
As $t=2$ sec
$\therefore V=\frac{1}{2}=0.5 \mathrm{m} / \mathrm{s}$
Download our appand 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.*
Similar Questions
- 1Which of the following is not true for this progressive wave $y = 4\sin 2\pi \left( {\frac{t}{{0.02}} - \frac{x}{{100}}} \right)$ where $y$ and $x$ are in $cm$ & $t$ in $sec$View Solution
- 2The fundamental frequency of a closed organ pipe of length $20\; cm$ is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is ...... $cm$View Solution
- 3Two sources $A$ and $B$ are sounding notes of frequency $660 \,Hz$. $A$ listener moves from $A$ to $B$ with a constant velocity $u$. If the speed of sound is $330 \,m / s$, what must be the value of $u$ so that he hears $8$ beats per second is .......... $m / s$View Solution
- 4A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440\, Hz$ to $480 \,Hz ,$ when it gets reflected from the wall. If the speed of sound in air is $345 \,m / s ,$ then the speed of the car is $.......km/hr$View Solution
- 5Velocity of sound in vacuum is .... $ms^{-1}$View Solution
- 6Two vibrating tuning forks produce progressive waves given by $y_1= 4 \sin (500 \, \pi t)$ and $y_2= 2 \sin (506 \, \pi t)$. These tuning forks are held near the ear of a person. The person will hearView Solution
- 7In a resonance tube experiment when the tube is filled with water up to height of $17.0\, cm$ from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5\, cm$. If the velocity of sound in air is $330\, m / s ,$ the tuning fork frequency is$......Hz$View Solution
- 8A tuning fork gives $5$ beats with another tuning fork of frequency $100\,Hz.$ When the first tuning fork is loaded with wax, then the number of beats remains unchanged, then what will be the frequency of the first tuning fork ..... $Hz$View Solution
- 9A source of unknown frequency gives $4\,\, beats/s$ when sounded with a source of known frequency $250\,\, Hz.$ The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency $513\,\, Hz.$ The unknown frequency is .... $Hz$View Solution
- 10At which temperature the speed of sound in hydrogen will be same as that of speed of sound in oxygen at $100\,^oC$ ..... $^oC$View Solution