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qUESTIONS

12th-MH

A string is fixed at both ends. What is the ratio of the frequency of the first harmonic to that of the second harmonic?

12th-MH

A closed pipe and an open pipe have the same length. Show that no mode of the closed pipe has the same wave length as any mode of the open pipe.

12th-MH

An air column 1s of length17 cm long. Calculate the frequency of 5% overtone if the air column is (a) closed atone end and (b) open at both ends. (Velocity of sound 1n air = 340 ms⁻¹)

12th-MH

Find the distance betweentwo successive nodes in a stationary waveon a string vibrating with frequency 64Hz. The velocity of progressive wave that resulted 1n the stationary wave 1s 48 ms⁻¹

12th-MH

A progressive wave travel son a stretched string. A particle on this string takes 4.0 ms to move from its mean position to one of its extreme positions. The distance between two consecutive points on the string which are at their mean positions(at a certain time instant) is 2.0 cm. Find the frequency. wavelength and speed of the wave.

12th-MH

The displacements of two sinusoidal waves propagating through a string arc given by the following equations y1 =4sin(20x – 30t) y2 =4sin(25x – 40t)where x and y are in centimeter and t is in second. a) Calculate the phase difference between these two waves at the points x = 5 cm and t  = 2s. b) When these two waves interfere, what are the maximum and minimum values of the intensity?

12th-MH

A wooden block of mass m is kept on a piston that can perform vertical vibrations of adjustable frequency and amplitude. During vibrations, we don’t want the block to leave the contact with the πston. How much maximum frequency is possible if the amplitude of vibrations is restricted to 25 cm? In this case, how much is the energy per unit mass of the block? (g ≈ π² ≈ 10 m s²)

12th-MH

Find the number of oscillations performed per minute by a magnet is vibrating in the plane of a uniform field of 1.6 × 10-5 Wb/m². The magnet has moment of inertia 3 * 10² – 6 * kg / (m² ) and magnetic moment 3A * m²  .

12th-MH

A 20 cm wide thin circular disc of mass 200 g is suspended to a rigid support from a thin metallic string. By holding the rim of the disc, the string is twisted through 60º and released. It now performs angular oscillations of period 1 second. Calculate the maximum restoring torque generated in the string under undamped conditions. (π² ≈ 31)

12th-MH

Two parallel S.H.M.s represented by x_{1} = 5sin(4πt + π / 3) cm and x_{2} =3 sin (4πt + π / 4) cm are superposed on a particle. Determine the amplitude and epoch of the resultant S.H.Μ.

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