KEAM 2014 Physics and Chemistry Paper

Given,
y1=A‌sin[k(x+ct)].....(i)
and ‌‌y2=A‌sin[k(x−ct)].....(ii)
By the principle of superposition, the resultant displacement of the particle is given by
y=y1+y2
y=A[sin{k(x+ct)}+sin{k(x−ct)}]
By the formula
We have
Y=2A‌sin‌k‌x⋅cos‌k‌c‌t
For first antinode
sin‌k‌x1=1
sin‌k‌x1=sin‌

π

2

kx1=‌

π

2

....(iii)
For second antinode
sin‌k‌x2=−1
sin‌k‌x2=sin‌

3π

2

kx2=‌

3π

2

......(iv)
∴ The distance between adjacent antinodes
kx2−kx1=‌

3π

2

−‌

π

2

k(x2−x1)=π
∆x=‌

π

k