Home
Class 12
PHYSICS
A rope of length L and mass m hangs free...

A rope of length L and mass m hangs freely from the ceiling. The velocity of transverse wave as a function of position x-along the rope is proportional to

A

`x^(0)`

B

`sqrt(x)`

C

`(1)/(sqrt(x))`

D

x

Text Solution

AI Generated Solution

To solve the problem, we need to find the velocity of a transverse wave along a rope of length \( L \) and mass \( m \) that hangs freely from a ceiling. The velocity of the wave will depend on the tension in the rope, which varies along its length due to the weight of the rope below the point of interest. ### Step-by-Step Solution: 1. **Understanding the Setup**: - Consider a rope of length \( L \) and mass \( m \) hanging vertically from a ceiling. - We want to analyze the wave velocity at a position \( x \) from the bottom of the rope. ...
Promotional Banner

Topper's Solved these Questions

  • WAVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section-A)|55 Videos

  • WAVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section-B)|35 Videos

  • WAVES

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT ( SECTION-D ( Assertion - Reason Type Questions ))|12 Videos

  • WAVE OPTICS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section-J (Aakash Challengers question))|1 Videos

  • WORK, ENERGY AND POWER

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - D)|13 Videos

Similar Questions

Explore conceptually related problems

A string of length L and mass M hangs freely from a fixed point . Calculate the velocity of the transverse wave along the string at any position. (b)Calculate time taken by a transverse pulse to traverse the string.

A heavy but uniform rope of lenth L is suspended from a ceiling. (a) Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end. (b) If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach teh celling ? (c ) A particle is dropped from the ceiling at the instant the bottom end is given the jerk where will the particle meet the pulse ?

A uniform rope of mass m and length L hangs from a celling. (a) Show that the speed of a transverse wave on the rope is a function of y , the distance from the lower end, and is given by t = 2sqrt(L//g) .

A uniform rope of legnth L and mass m_1 hangs vertically from a rigid support. A block of mass m_2 is attached to the free end of the rope. A transverse pulse of wavelength lamda_1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is lamda_2 . The ratio (lamda_2)/(lamda_1) is

A uniform rope of elngth l and mass m hangs vertically from a rigid support. A block of mass m is attached to the free end of the rope. A transverse pulse of wavelength lambda is produced at the lower end of the rope. The wavelength of the pulse, when it reaches the top of the rope. is alambda . Find a^(2)

A uniform rope of length 12 m and mass 4 kg is hung vertically from a rigid support transverse wave pulse is produced at lower end. The speed of the wave pulse al x = 2.5 m from lower and will be kg=10 m/s)

A uniform rope of mass m hangs freely from a ceiling. A bird of mass M climbs up the rope with an acceleration a. The force exerted by the rope on the ceiling is

A uniform rope of mass M=0.1kg and length L=10m hangs from the celling. [g=10m//s^(2)] :- (1)speed of transverse wave in the rope increases linearly from top to the bottom. (2)speed of the transverse wave in the rope decreases linearly from bottom to the top. (3)speed of the transverse wave in the rope remain constant along the length of the rope (4)time taken by the transverse wave to travel the full length of the rope is 2 sec.

A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. (a) Find the speed of transverse wave in the rope at a point 0.5 m distant from the lower end. (b) Calculate the time taken by a transverse wave to travel the full length of the rope.

A uniform rope of length 12 mm and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?

AAKASH INSTITUTE ENGLISH-WAVES-Try Yourself
  1. A body executing shm completes 120 oscillations per minute. If the amp...

    Text Solution

    |

  2. A block of mass M is kept in elevator (lift) which starts moving upwar...

    Text Solution

    |

  3. A rope of length L and mass m hangs freely from the ceiling. The veloc...

    Text Solution

    |

  4. Find the temperature at which the velocity of sound in air is double t...

    Text Solution

    |

  5. Explain why transver waves cannot be propagated through fluids?

    Text Solution

    |

  6. What is common in mechanical longitudinal and transverse waves?

    Text Solution

    |

  7. The frequency of a mechanical wave is 256 Hz. Calculate its wavelength...

    Text Solution

    |

  8. A mechanical wave has a velocity of 330 m/s. calculate its frequency i...

    Text Solution

    |

  9. A steel wire 100 cm long has a mass of 10 gm. If the wire is under a t...

    Text Solution

    |

  10. What is the speed of a transverse wave in a rope of length 10 m and ma...

    Text Solution

    |

  11. Calculate the speed of longitudinal sound wave in a liquid. The bulk m...

    Text Solution

    |

  12. The speed of longitudinal mechanical wave in a material is 4300 m/s. y...

    Text Solution

    |

  13. The speed of sound waves in air at 300K is 332 m/s. At what temperatur...

    Text Solution

    |

  14. The velocity of sound in air at 20^(@)C is 340ms^(-1). Keeping the tem...

    Text Solution

    |

  15. Two waves represented by y(i)=3sin(200x-150t) and y(2)=3cos(200x-150t)...

    Text Solution

    |

  16. What is the phase difference between two waves of equal amplitude havi...

    Text Solution

    |

  17. A man fires a gun while standing between two parallel hills. If he hea...

    Text Solution

    |

  18. The equation of a transverse wave travelling along a string is y(xt)=0...

    Text Solution

    |

  19. The equation of a stationary wave is represented by y=2sin((2pix)/(3...

    Text Solution

    |

  20. A sonometer wire is under a tension of 10 N and the length between the...

    Text Solution

    |