The displacement equations of two interfering waves are given by

$y_1  =10 \sin \left(\omega t+\frac{\pi}{3}\right) cm$

$y_2 =5[\sin (\omega t)+\sqrt{3} \cos \omega t] \;cm$ respectively.

The amplitude of the resultant wave is $.............cm$.

  • A$18$
  • B$17$
  • C$20$
  • D$16$
JEE MAIN 2023, Diffcult
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 mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude $A.$ Its speed as it passes through the equilibrium position is $V.$ If extended $2A$ and released, the speed of the mass passing through the equilibrium position will be
    View Solution
  • 2
    The length of a simple pendulum is increased by $1\%$. Its time period will
    View Solution
  • 3
    A cylindrical block of wood (density $= 650\, kg\, m^{-3}$), of base area $30\,cm^2$ and height $54\, cm$, floats in a liquid of density $900\, kg\, m^{-3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... $cm$ (nearly)
    View Solution
  • 4
    A mass $m$ is vertically suspended from a spring of negligible mass; the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4 m$ is suspended from the same spring
    View Solution
  • 5
    The displacement $x$ (in metre) of a particle in, simple harmonic motion is related to time t (in seconds) as

    $x = 0.01\cos \left( {\pi \,t + \frac{\pi }{4}} \right)$

    The frequency of the motion will be

    View Solution
  • 6
    The length of the second pendulum on the surface of earth is $1\, m$. The length of seconds pendulum on the surface of moon, where g is 1/6th value of $g$ on the surface of earth, is
    View Solution
  • 7
    $Assertion :$ For a particle performing $SHM$, its speed decreases as it goes away from the mean position.
    $Reason :$ In $SHM$, the acceleration is always opposite to the velocity of the particle.
    View Solution
  • 8
    A particle moves in the $x-y$ plane according to equation $\overrightarrow r  = (\widehat i + 2\widehat j)\, A \, \cos \omega t$. The  motion of the particle is 
    View Solution
  • 9
    Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $K _{1}$ and $K _{2}$ respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of $A$ and $B$ is
    View Solution
  • 10
    If the speed $v$ of the bob in a simple pendulum is plotted against the tangential acceleration $a$, the correct graph will be represented by
    View Solution