JEE Main Oscillations & Waves PYQ (2002–2026)

5 real JEE Main questions on Oscillations & Waves, straight from past papers. Try them, then check the answer.

1. Q1JEE Main 2026 (Online) 23rd January Morning Shift

   A simple pendulum of string length 30 cm performs 20 oscillations in 10 s . The length of the string required for the pendulum to perform 40 oscillations in the same time duration is

   $\_\_\_\_$ cm . [Assume that the mass of the pendulum remains same.]

   1. A

      0.75

   2. B

      7.5

   3. C

      15

   4. D

      120

   Show answer Step-by-step solution — free with sign-up
2. Q2JEE Main 2026 (Online) 21st January Morning Shift

   Two strings $(A, B)$ having linear densities $\mu_A$​${}=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B$​${}=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and lengths $L_A$​${}=2.5 \mathrm{~m}$ and $L_B$​${}=1.5 \mathrm{~m}$ respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1 / t_2$ is:

   1. A

      1.90

   2. B

      1.18

   3. C

      1.08

   4. D

      1.67

   Show answer Step-by-step solution — free with sign-up
3. Q3JEE Main 2025 (Online) 4th April Morning Shift

   Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

   1. A
      $\theta_1 l_2$​${}=\theta_2 l_1$
   2. B
      $\theta_1 l_1$​${}=\theta_2 l_2$
   3. C
      $\theta_1 l_2^2$​${}=\theta_2 l_1^2$
   4. D
      $\theta_1 l_1^2$​${}=\theta_2 l_2^2$
   Show answer Step-by-step solution — free with sign-up
4. Q4JEE Main 2025 (Online) 2nd April Evening Shift
   A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x$​${}=0$ at $\mathrm{t}$​${}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?
   1. A
      $y$​${}=2 \cos (0.83 x-3.35 t) \mathrm{cm}$
   2. B
      $y$​${}=2 \sin (0.83 x-3.5 \mathrm{t}) \mathrm{cm}$
   3. C
      $y$​${}=2 \cos (0.13 x-0.5 t) \mathrm{cm}$
   4. D
      $y$​${}=2 \cos (3.35 x-0.83 \mathrm{t}) \mathrm{cm}$
   Show answer Step-by-step solution — free with sign-up
5. Q5JEE Main 2024 (Online) 9th April Morning Shift

   The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$ and $16 \mathrm{~ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x}, \mathrm{~m}$ where $x$ is _________.

   Show answer Step-by-step solution — free with sign-up