1.

A sine wave has an amplitude A and a wavelength λ. Let V be the wave velocity, and v be maximum velocity of a particle in the medium. (a) V cannot be equal to v (b) V = v, if A = λ/2π (c) V = v, if A = 2πλ(d) V = v, if λ = A/π

Answer»

Correct Answer is: (b) V = v, if A = λ/2π 

y = Asin(ωt - kx) 

ω = 2πn,  

k = 2π/λ, 

where n = frequency and λ = wavelength.

Wave velocity = V = nλ = ω/k.

Particle velocity = dy/dt = Aωcos(ωt - kx).

∴ maximum particle velocity = v = Aω.

For V = v1, ω/k = Aω

or A = 1/k =  λ/2π.



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