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Q.

The angular frequency of a particle in a progressive wave in an elastic medium is $100 π {rads}^{- 1}$ and it is moving with a velocity of $200 {ms}^{- 1}$ . The phase difference between two particles separated by a distance of 20 m is

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a

36 rad

b

31.4 rad

c

$π$ rad

d

3 $π$ /4 rad

answer is A.

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Detailed Solution

w = 100 $π$ rad/s ; V = 200m/s ; $∆$ x = 20m
Phase diff $∆ ϕ = \frac{2 π}{λ} ∆ x$
w = 2 $π$ n = 100 $π$ $\Rightarrow$ n = 50Hz
$v = nλ \Rightarrow λ = \frac{v}{n} = \frac{200}{50} = 4 m ∆ ϕ = \frac{2 π}{4} (20) = 10 π = 10 x 3.14 = 31.4 rad$

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