SHM & Waves – JEE Main 2026 Quiz

Q1. A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz under a certain tension. The resonating length of the same wire for fundamental frequency 600 Hz under the same tension is ____ cm.

Q2. In a resonance experiment, two air columns closed at one end have lengths 100 cm and 120 cm. When each vibrates in its fundamental mode, 15 beats per second are produced. The velocity of sound in air is:

Q3. Two harmonic waves travelling in the same direction superpose to give the resultant wave x = a cos(1.5t) cos(50.5t), where t is in seconds. The time period of beats (nearest integer) is:

Q4. The magnitudes of displacement, velocity and acceleration of a particle executing SHM at a certain instant are 4 m, 2 m s⁻¹ and 16 m s⁻² respectively. If the amplitude is √x m, find x.

Q5. The displacement of a particle executing SHM is given by x = 10 sin(ωt + π/3) m. If the time period is 3.14 s, then the velocity of the particle at t = 0 is ____ m/s.

Q6. A particle executes SHM with time period 2 s and amplitude 1 cm. If D and d are the total distance and displacement covered in 12.5 s, then D/d is:

Q7. Two bodies A and B of equal mass are suspended from two massless springs of spring constants k₁ and k₂ respectively. If both oscillate vertically with equal amplitudes, the ratio of their maximum velocities vₐ / vᵦ is:

Q8. A plane progressive wave is represented by y = 2 cos[2π(330t − x)]. The frequency of the wave is:

Q9. Two simple pendulums of lengths l₁ and l₂ undergo angular displacements θ₁ and θ₂ from their mean positions. If their angular accelerations are equal, then which relation is correct?

Q10. A closed organ pipe and an open organ pipe are filled with gases having the same bulk modulus but densities in the ratio ρ₁ : ρ₂ = 1 : 16. The frequency of the 9th harmonic of the closed pipe is equal to the frequency of the 4th harmonic of the open pipe. If the length of the closed pipe is 10 cm, the length of the open pipe is: