HARD
JEE Main
IMPORTANT
Earn 100

A string of mass m is fixed at both ends. The fundamental tone oscillations are excited with circular frequency ω and maximum displacement amplitude amax. Find:

(a) the maximum kinetic energy of the string;

(b) the mean kinetic energy of the string averaged over one oscillation period.

Important Questions on OSCILLATIONS AND WAVES

HARD
JEE Main
IMPORTANT
A standing wave ξ=a sinkx×cosωt is maintained in a homogeneous rod with cross-sectional area S and density ρ. Find the total mechanical energy confined between the sections corresponding to the adjacent displacement nodes.
HARD
JEE Main
IMPORTANT
A source of sonic oscillations with frequency f0=1000 Hz, moves at right angles to the wall with a velocity u=0.17 m s-1. Two stationary receivers R1 and R2 are located on a straight line, coinciding with the trajectory of the source, in the following succession: R1-source-R2-wall. Which receiver registers the beatings and what is the beat frequency? The velocity of sound is equal to v=340 m s-1.
HARD
JEE Main
IMPORTANT

A stationary observer receives sonic oscillations from two tuning forks, one of which approaches, and the other recedes with the same velocity. As this takes place, the observer hears the beatings with frequency fB=2.0 Hz. Find the velocity of each tuning fork if their oscillation frequency is f0=680 Hz and the velocity of sound in air is v=340 m s-1.

HARD
JEE Main
IMPORTANT
A receiver and a source of sonic oscillations of frequency f0=2000 Hz are located on the x-axis. The source swings harmonically along that axis with a circular frequency ω and an amplitude a=50 cm. At what value of ω will the frequency bandwidth registered by the stationary receiver be equal to Δf=200 Hz? The velocity of sound is equal to v=340 m s-1.
HARD
JEE Main
IMPORTANT
A source of sonic oscillations with frequency f0=1700 Hz and a receiver are located at the same point. At the moment t=0, the source starts receding from the receiver with constant acceleration w=10.0 m s-2. Assuming the velocity of sound to be equal to v=340 m s-1, find the oscillation frequency registered by the stationary receiver, t=10.0 s after the start of motion.
HARD
JEE Main
IMPORTANT

A source of sound with natural frequency f0=1.8 kHz moves uniformly along a straight line, separated from a stationary observer by a distance l=250 m. The velocity of the source is equal to η=0.80 fraction of the velocity of sound. Find:

(a) the frequency of sound received by the observer at the moment when the source gets closest to him;

(b) the distance between the source and the observer at the moment when the observer receives a frequency f=f0.

HARD
JEE Main
IMPORTANT
A stationary source sends forth monochromatic sound. A wall approaches it with velocity u=33  cm s-1. The propagation velocity of sound in the medium is v=330 m s-1. In what way and how much, in per cent, does the wavelength of sound change on reflection from the wall?
HARD
JEE Main
IMPORTANT
A source of sonic oscillations with frequency f0=1700 Hz and a receiver are located on the same normal to a wall. Both the source and the receiver are stationary, and the wall recedes from the source with velocity u=6.0 cm s-1. Find the beat frequency registered by the receiver. The velocity of sound is equal to v=340 m s-1.