wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Two travelling waves, y1=Asin[k(x+ct)] and y2=Asin[k(xct)] are superposed on string. The distance between adjacent antinodes is :

A
ctπ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
ct2π
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
π2k
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
kπ
No worries! We‘ve got your back. Try BYJU‘S free classes today!
E
πk
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is E πk
Given,
Y1=Asin[k(x+ct)] ...(i)
and Y2=Asin[k(xct)] .. .(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(xct)}]
By the formula
sinC+sinD=2sinC+D2cosCD2
We have Y=2Asinkx+kct+kxkct2coskx+kctkx+kct2
y=2Asinkxcoskct
For first antinode
sinkx1=1
sinkx1=sinπ2
kx1=π2 ...(iii)
For second antinode
sinkx2=1
sinkx2=sin3π2
kx2=3π2 (iv)
The distance between adjacent antinodes
kx2kx1=3π2π2
k(x2x1)=π
Δx=πk

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Wave Interference
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon