A Particle Is Executing Simple Harmonic Motion Along The x-axis With Amplitude 4 Cm And Time Period 1.2 S. The Minimum Time Taken By The Particle To Move From x = +2 Cm To x = +4 Cm And Back Again Is

A train blowing its whistle moves with a constant velocity u away from the observer on the ground. The ratio of the actual frequency of the whistle to that measured by the observer is found to be 1.2. If the train is at rest and the observer moves away from it at the same velocity, the ratio would be given by

The intensity of sound gets reduced by 20% on passing through a slab. The reduction in intensity on passage through two consecutive slabs is

Two sounding bodies producing progressive waves given by 

are situated very near to the ears of a person who will hear

An organ pipe P₁, closed at one end vibrating in its first harmonic and another pipe P₂, open at both ends vibrating in its third harmonic, are in resonance with a given tuning fork. The ratio of the lengths of P₁ and P₂is

Two identical straight wires are stretched so to produce 6 beats per second when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by T₁ andT₂ the higher and the lower initial tensions in the strings, then it could be said that while making the above changes in tension.

The time taken by a particle executing simple harmonic motion of time period T to move from the mean position to half the maximum displacement is

To raise the pitch of a stringed musical instrument, the player can

One end a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young’s modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period given by

A weight is attached to the free end of a sonometer wire. Resonance occurs at a length of 40 cm of the wire with a tuning fork of frequency 512 Hz. The weight is then immersed wholly in water, the resonant length is reduced to 30 cm. The relative density of the weight is

Two waves are represented by the following equations:

The ratio of intensities I₂/I₁ will be