A car is moving towards a high cliff. The driver sounds a horn of frequency $$f$$. The reflected sound heard by the driver has frequency $$2f$$. If v is the velocity of sound, then the velocity of the car, in the same velocity units, will be

The phase difference between two waves. represented by
y₁ = 10^$$-$$6 sin[100t + (x/50) + 0.5] m
y₂ = 10^$$-$$6 cos[100t + (x/50)] m,
where x is expressed in metres and t is exressed in secondss, is approximately.

An observer moves towards a stationary source of sound with a speed 1/5^th of the speed of sound. The wavelength and frequency of the source emitted are $$\lambda $$ and $$f$$ respectively. The apparent frequency and wavelength recorded by the observer are respectively

A whistle revolves in a circle with angular speed $$\omega $$ = 20 rad/s using a string of length 50 cm. If the frequency of sound from the whistle is 385 Hz, then what is the minimum frequency heard by an observer which is far away from the centre (velocity of sound $$=$$ 340 m/s)