The equation of a simple harmonic wave is given by

y = 3 sin$${\pi \over 2}$$(50t $$-$$ x),

where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

A train moving at a speed of 220 m s^$$-$$1 towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is
(Speed of sound in air is 330 m s^$$-$$1)

Two sources of sound placed close to each other, are emitting progressive waves given by
y₁ = 4sin600$$\pi $$t and y₂ = 5sin608$$\pi $$t
An observer located near these two sources of sound will hear

When a string is divided into three segments of length $$l$$₁, $$l$$₂ and $$l$$₃ the fundamental frequencies of these three segments are $${\upsilon _1},{\upsilon _2}$$ and $${\upsilon _3}$$ respectively. The original fundamental frequency ($$v$$) of the string is