Home
Class 11
PHYSICS
The vibrations of a string of length 60 ...

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation `y=4sin((pix)/15) cos (96 pi t)`, where x and y are in cm and t in seconds.
(a)What is the maximum displacement of a point at `x = 5cm`?
(b)Where are the nodes located along the string?
(c)What is the velocity of the particle at x=7.5cm and t=0.25s?
(d)Write down the equations of the component waves whose superposition gives the above wave.

Text Solution

Verified by Experts

The correct Answer is:
A
(a) At `x=5cm`, the standing wave equation gives
`y=4sin((5pi)/15)cos(96pit)`
`=4sin(pi/3)cos (96pit)`
`=4xx sqrt3/2 cos(96pit)`
`:. Maximum displacement =`2sqrt3` cm
(b)The nodes are the points of permanent rest. Thus, they are those points for which
` sin((pix)/(15))=0`
i.e. `(pix)/(15) =npi`, where `n=0,1,2,3,4`...................
`x=15n`, i.e. at `x=0,15,30,45` and `60 cm`,
(c) The particle velocity is equal to
`((dely)/(delt)) = 4sin ((pix)/(15)) (96pi) (-sin 96pi t)`
=-`384 pi sin ((pix)/(15)) (-sin 96pit)`
At `x=7.5 cm` and `t=0.25 s`, we get
`(((dely)/(delt)))= -384 pi sin (pi/2)sin (24pi)=0`
(d)The equations of the component waves are
`y_(1) = 2sin (((pix)/15)+96pit)`
and `y_(2) = 2sin((pix)/(15) - 96pit)`
as we can see that `y=(y_1+y_2)` .
Promotional Banner

Topper's Solved these Questions

  • SUPERPOSITION OF WAVES

    DC PANDEY|Exercise Example Type 1|1 Videos

  • SUPERPOSITION OF WAVES

    DC PANDEY|Exercise Example Type 2|1 Videos

  • SOUND WAVES

    DC PANDEY|Exercise Exercise 19.7|4 Videos

  • THERMOMETRY THERMAL EXPANSION AND KINETIC THEORY OF GASES

    DC PANDEY|Exercise Medical entrance gallary|30 Videos

Similar Questions

Explore conceptually related problems

The vibrations of a string of length 600cm fixed at both ends are represented by the equation y=4 sin (pi (x)/(15)) cos (96 pi t ) where x and y are in cm and t in seconds.

The vibrations of a string of length 60 cm fixed at both ends are represented by the equation y=4 sin (pix//15) cos (96 pit) where x and y are in cm and t in seconds. The maximum displacement at x = 5 cm is–

The vibrations of a string of length 60cm fixed at both ends are represented by the equation---------------------------- y = 4 sin ((pix)/(15)) cos (96 pit) Where x and y are in cm and t in seconds. (i) What is the maximum displacement of a point at x = 5cm ? (ii) Where are the nodes located along the string? (iii) What is the velocity of the particle at x = 7.5 cm at t = 0.25 sec .? (iv) Write down the equations of the component waves whose superpositions gives the above wave

The vibrations of string of length 60 cm fixed at both ends are presented by the equations y = 4 sin ( pi x//15) cos ( 96 pi t) where x and y are in cm and t in s . The maximum displacement at x = 5 cm is

The vibration of a string of length 60cm fixed at both ends are represented by displacedment y=4sin ((pix)/(15)) cos (96pi) where x and y are in cm and t in second. The particle velocity at x=22.5 and t=0.25 is

The vibrations of a string of length 60 cm fixed at both the ends are represented by the equation y = 2 "sin"((4pix)/(15)) "cos" (96 pit) where x and y are in cm. The maximum number of loops that can be formed in it is

The vibrations of a string fixed at both ends are represented by y=16sin((pix)/(15))cos(96pit) . Where 'x' and 'y' are in cm and 't' in seconds. Then the phase difference between the points at x=13cm and x=16 in radian is

The vibration of a string of length 60 cm is represented by the equation, y = 3 cos (pix//20) cos(72pit) where x & y are in cm and t in sec. (i) Write down the compoent waves whose superposition gives the above wave. (ii) Where are the nodes and antinodes located along the string. (iii) What is the velocity of the particle of the string at the position x = 5 cm & t = 0.25 sec.