Question

A wave is represented by the equation y = 0.20 sin [ 0.4π (x – 60t)], where x and y are in cm and t is in s. The velocity of the wave is..

Answer 1

Answer:

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y1 = 2 sin 2π[100t –x/ 60 ]cm

y2= y1 = 2 sin 2π[ 100t +x/ 60] cm

Formula : Y= R sin2 πnt

Where R=2A Cos [2 πx/ λ]

Now resultant equation is  

Y= y1+y2

=2sin2 π (100t-x/60] + 2sin 2 π[100t+x/60]

Y=2x2sin2 π(100t)cos2 π(x/60]

Y=4cos (2 πx/60)sin 2 π(100t)

On comparing the above equation with  

Y=Rsin(2 πt)

4cos (2πx/60)=R

But R=2 πcos(2 πR/ λ)

Since λ=60cm

R is maximum when Cos (2 πR/ λ)=1

R=4x1=4cm

Λ=60m

λ/4=60/4=15cm

Therefore distance between  successive node and anti node is 15cm

Length= λ/2=60/2=30cm

Similarly =v=n λ

N=100hz

A=60cm

V=100x60=600cm/s

V=60m/s