A stationary wave is represented by $y=A \sin (100 t) \cos (0.01 x)$, where $y$ and $A$ are in millimetres, $t$ is in second and $x$ is in metre. The velocity of the constituent wave is ........... $m / s$
Easy
Download our app for free and get startedPlay store
(a)

$y=A \sin 100 t \cos 0.01 x$

$\omega=100 \quad k=0.01$

$v=\frac{\omega}{k}$

$\text { or } v=10^4 \,m / s$

art

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.*

Similar Questions

  • 1
    A train, standing in a station-yard, blows a whistle of frequency $400\,Hz$ in still air. The wind starts blowing in the direction from the yard to the station with a speed of $10\,ms^{-1}$ then value of frequency and speed of sound for observer will be (the speed of sound in still is $340\, ms^{-1}$ )
    View Solution
  • 2
    A wave of frequency $100 Hz$ is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of $10 cm$ from the fixed end of the string. The speed of incident (and reflected) wave are .... $m/s$
    View Solution
  • 3
    The relation between time and displacement for two particles is given by

    ${y_1} = 0.06\sin 2\pi (1.04t + {\phi _1})$,

    ${y_2} = 0.03\sin 2\pi (1.04t + {\phi _2})$

    The ratio of the intensity of the waves produced by the vibrations of the two particles will be

    View Solution
  • 4
    Two trains, one coming towards and another going away from an observer both at $4\; m/s$ produce whistle simultaneously of frequency $300 \;Hz$. Find the number of beats produced
    View Solution
  • 5
    A stationary source is emitting sound at a fixed frequency $\mathrm{f}_0$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2 \%$ of $f_0$. What is the difference in the speeds of the cars (in $\mathrm{km}$ per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is $330 \mathrm{~ms}^{-1}$.
    View Solution
  • 6
    A transverse progressive wave on a stretched string has a velocity of $10\,m{s^{ - 1}}$ and a frequency of $100 Hz.$ The phase difference between two particles of the string which are $2.5 cm$ apart will be
    View Solution
  • 7
    A uniform string resonates with a tuning fork, at a maximum tension of $32 \,N$. If it is divided into two segments by placing a wedge at a distance one-fourth of length from one end, then to resonance with same frequency the maximum value of tension for string will be ........... $N$
    View Solution
  • 8
    A plane wave is described by the equation $y = 3\cos \left( {\frac{x}{4} - 10t - \frac{\pi }{2}} \right)$. The maximum velocity of the particles of the medium due to this wave is
    View Solution
  • 9
    A steel rod $100 cm$ long is clamped at its mid-point. The funda-mental frequency of longitudinal vibrations of the rod is given to be $2.53 kHz$. What is the speed of sound in steel .... $km/s$
    View Solution
  • 10
    The vibration of a string fixed at both ends are described by $Y= 2 \,\,sin(\pi x) \,\,sin\,\,(100\pi t)$ where $Y$ is in $mm$,$x$ is in $cm$,$t$ in $sec$ then
    View Solution