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
    The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10\,s^{-1}$.  At, $t = 0$ the displacement is $5\, m$. What is the maximum acceleration ? The initial phase is $\frac{\pi }{4}$
    View Solution
  • 2
    The motion of a simple pendulum excuting $S.H.M$. is represented by following equation.

    $Y = A \sin (\pi t +\phi)$, where time is measured in $second$.

    The length of pendulum is .............$cm$

    View Solution
  • 3
    A particle moves on $x-$ axis according to the equation $x = x_0\,\,sin^2\,\omega t,$  the motion is simple harmonic
    View Solution
  • 4
    The displacements of two particles executing $S.H.M.$ on the same line are given. as $y_1=a \sin \left(\frac{\pi}{2} t+\phi\right)$ and $y_2=b \sin \left(\frac{2 \pi}{3} t+\phi\right)$. The phase difference between them at $t=1 \,s$ is .........
    View Solution
  • 5
    Velocity at mean position of a particle executing $S.H.M.$ is $v$, they velocity of the particle at a distance equal to half of the amplitude
    View Solution
  • 6
    A body of mass $m $ is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass $m$ is slightly pulled down and released , it oscillates with a time period of $3\,s$ . When the mass $m$ is increased by $1\,kg$ , the time period of oscillations becomes $5\,s$ . The value of $m$ in $kg$ is
    View Solution
  • 7
    A weightless spring which has a force constant oscillates with frequency $n$ when a mass $m$ is suspended from it. The spring is cut into two equal halves and a mass $2m $ is suspended from it. The frequency of oscillation will now become
    View Solution
  • 8
    The graph in figure represents
    View Solution
  • 9
    The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\  N/m.$ The particles are pulled to the right and then released from the  positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\  kg$ and $m_2 = 27 \,kg \,?$
    View Solution
  • 10
    A particle performs $SHM$ with a period $T$ and amplitude $a.$ The mean velocity of the particle over the time interval during which it travels a distance $a/2$ from the extreme position is
    View Solution