A transverse wave is described by the equation y=Y0sin2πft-2πλx. The maximum particle velocity is four times the wave velocity if :

(1) λ=πY04

(2) λ=πY02

(3) λ=πY0

(4) λ=2πY0

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Types of waves
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A transverse wave of amplitude 0.5 m and wavelength 1 m and frequency 2 Hz is propagating in a string in the negative x-direction. The expression for this wave is :

(1) y(x,t)=0.5sin(2πx4πt)

(2) y(x,t)=0.5cos(2πx+4πt)

(3) y(x,t)=0.5sin(πx2πt)

(4) y(x,t)=0.5cos(2πx+2πt)

Concept Questions :-

Types of waves
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The displacement of a particle is given by y=5×104sin(100t50x), where x is in meter and t is in  sec, find out the velocity of the wave :

(1) 5000 m/sec

(2) 2 m/sec

(3) 0.5 m/sec

(4) 300 m/sec

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Which one of the following does not represent a traveling wave :

(1) y=sin(xvt)

(2) y=ymsink(x+vt)

(3) y=ymsin(xvt)

(4) y=f(x2vt2)

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Wave equations of two particles are given by y1=asin(ωtkx), y2=asin(kx+ωt), then :

(1) They are moving in the opposite direction

(2) The phase between them is 90°

(3) The phase between them is 180°

(4) The phase between them is 0°

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A transverse wave is represented by the equation y=y0sin2πλ(vtx)

For what value of λ, the maximum particle velocity equal to two times the wave velocity?

(1) λ=2πy0

(2) λ=πy0/3

(3) λ=πy0/2

(4) λ=πy0

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A wave travels in a medium according to the equation of displacement given by y(x,t)=0.03sinπ(2t0.01x) where y and x are in metres and t in seconds. The wavelength of the wave is :

(1) 200 m

(2) 100 m

(3) 20 m

(4) 10 m

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Equation of a progressive wave is given by y=4sinπt5x9+π6

Then which of the following is correct ?

(1) v = 5 m / sec

(2) λ = 18 m

(3) a = 0.04 m

(4) n = 50 Hz

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The frequency of the sinusoidal wave y=0.40cos[2000t+0.80x] would be :

(1) 1000 π Hz

(2) 2000 Hz

(3) 20 Hz

(4) 1000πHz

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The equation of a plane progressive wave is given by y=0.025sin(100t+0.25x). The frequency of this wave would be :

(1) 50πHz

(2) 100πHz

(3) 100 Hz

(4) 50 Hz

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