A transverse wave is described by the equation
y =yo sin 2n(ft
Show that maximum particle velocity is equal to four times the wave velocity if A is equal to nyo/2

Calculate the velocity of sound in a gas in which two waves of wavelengths 2 m and 2·02 m produce 3 beats in 2 s.

Calculate the ratio of kinetic and potential energies when the displacement of an oscillating particle is equal to half of its amplitude.

Sound waves travelling in water are incident on a water-steel interface. The impedances of water and steel are 1·43 x 10^6 s and 3·9 x 10^7 s respectively. Calculate the percentage of sound energy reflected back into the water medium.

Obtain an expression for the frequency at which charge oscillates in an LC circuit.

The quality factor of a tuning fork of frequency 512 Hz is 4 X 10^4. Calculate the time in which its energy will reduce to of its energy in the absence of damping.

Can a function like fit) (sin wt cos wt) represent a simple harmonic motion If yes, what would be the time period, amplitude and initial phase of such a motion?

2. Attempt any two parts:

Derive relations for the apparent frequencies of sound

when the source moves towards the listener, and

when the listener moves towards the source. If the source velocity were same as the listener velocity, in which of these two cases would the Doppler shift be more?

Derive an expression for the time period of a vertically suspended spring-mass system. If this system is used in a clock to measure time, will this clock prove better or worse than a clock based on a simple pendulum, particularly when the clock is taken to moon

State the principle on which a flute works. Obtain an expression for the fundamental frequency of a flute.