IIT JEE , AIEEE Forum - Physics , Mechanics

shinee

the wave disturbance in a medium is described by y=0.02cos(50(pi)t +pi/2)cos(10(pi)x) where x and y are in meters and t in seconds
a) node occurs at x=0.15m                         b)an anti node occurs at x=0.3m
c)the speed of the wave is 5.0m/s                d)the wave length is 0.2m

1) only a and b are correct                            2)only a, b, d are correct
3)only b,c,d are correct                                4)All are correct

ans is 4) all are correct
but how, can u plz give the reasons (i could only prove that c is correct)
salute assured

pardesi

hint:
if y=Asin(wt-kx) and y=Asin(Kx+wt) be the waves which together produce standing waves then the equation of those waves becomes
y2Acos kx sin wt
speed of wave is w/k
wavelength is 2pi/k
also node occurs when x=(n+0.5)lambda/2
antidode at n\lambda/4
so just compare the coefficients of the expressions

also cos(x+\pi/2)=sin x

Conjurer

a)If cos(10(pi)x) is zero, then for any value of t,the position at x is a node.

cos@ is zero at 2npi +- pi/2

10pix = 2npi+-pi/2

x = n/5 +- 1/20

Put n =1 and use minus sign.

b)Similarly for antinode use cos@ = npi

c) You did it!

d) k = 2pi/lambda

10pi = 2pi/lambda, result follows

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