JEE Physics/ Lakshmikanta Satapathy/ Wave motion QA part 2/ JEE Question on wave pulse travelling along a string suspended from a support solved with related concepts

1. Physics Helpline
L K Satapathy
Wave Motion 2
Wave Pulse in a Vertical String
A
B
l

2. Physics Helpline
L K Satapathy
Wave Motion 2
Speed of a wave in a stretched string is given by
Question : A uniform string of length 20m is suspended from a rigid support. A short
wave pulse is introduced at its lower end. The time taken by it to reach the support
is (take )
Answer :
( ) 2 2 ( ) 2 ( ) 2 2 ( ) 2a s b s c s d s
2
10g m s
T
v


Where T = tension in the string ,  = mass /unit length
Let the length of the string = l , area of cross-section = A
Density of its material =   mass of string =
 Mass /unit length
Al
A  A
B
l=20m
The wave pulse is introduced at the lower end A

3. Physics Helpline
L K Satapathy
Wave Motion 2
dy dy
v gy dt
dt gy
    
0
0
1 1
2
l
ldy
t y
g y g
     
Correct option = (c)
A
B
P
y
Consider a point P at a distance y above A
 Tension in the string at P = weight of string below it T Ay g 
 The speed of the wave pulse at P is
T Ay g
v gy
A

 
  
Since v depends on y , time of journey has to be obtained by integration
2 2 20
2 2 sec
10
[ ]ns
l
g
A  
 Integrating from y = 0 to y = l

4. Physics Helpline
L K Satapathy
For More details:
www.physics-helpline.com
Subscribe our channel:
youtube.com/physics-helpline
Follow us on Facebook and Twitter:
facebook.com/physics-helpline
twitter.com/physics-helpline