Home
Class 11
PHYSICS
A steel wire of length 1m, mass 0.1kg an...

A steel wire of length `1m`, mass `0.1kg` and uniform cross-sectional area `10^(-6)m^(2)` is rigidly fixed at both ends. The temperature of the wire is lowered by `20^(@)C`. If transverse waves are set up by plucking the string in the middle.Calculate the frequency of the fundamental mode of vibration.
Given for steel `Y = 2 xx 10^(11)N//m^(2)`
`alpha = 1.21 xx 10^(-5) per ^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
11 Hz
For wire, `DeltaL=L alpha theta = (FL)/(AY)rArr D=AY alpha theta`
`:. f=(1)/(2L)sqrt((F)/(mu))=(1)/(2xx1)sqrt((10^(-6)xx2xx10^(11)xx1.21 xx10^(5)xx20)/(0.1))`
`=11Hz`
Promotional Banner

Topper's Solved these Questions

  • WAVES AND OSCILLATIONS

    ALLEN|Exercise Part-1(Exercise-04)[B]|13 Videos

  • WAVES AND OSCILLATIONS

    ALLEN|Exercise Part-1(Exercise-05)[A]|28 Videos

  • WAVES AND OSCILLATIONS

    ALLEN|Exercise Part-1(Exercise-03)|31 Videos

  • SEMICONDUCTORS

    ALLEN|Exercise Part-3(Exercise-4)|51 Videos

Similar Questions

Explore conceptually related problems

A steel wire of length 1m , mass 0.1kg and uniform cross-sectional area 10^(-6)m^(2) is rigidly fixed at both ends. The temperature of the wire is lowered by 20^(@)C . If transverse calculate the frequency of the fundamental mode of vibration. Given for steel Y = 2 xx 10^(11)N//m^(2) alpha = 1.21 xx 10^(-5) per ^(@)C

A steel wire of length 1 m and mass 0.1 kg and having a uniform cross-sectional area of 10^(-6) m^(2) is rigidly fixed at both ends. The temperature of the wire is lowered by 20^(@)C . If the wire is vibrating in fundamental mode, find the frequency (in Hz). (Y_(steel)=2xx 10^(11) N//m^(2),alpha_(steel)=1.21 xx 10^(-5)//.^(@)C) .

A steel wire of length 20 cm and uniform cross-sectional area of 1 mm^(2) is tied rigidly at both the ends at 45^(@)C . If the temperature of the wire is decreased to 20^(@)C , then the change in the tension of the wire will be [Y for steel = 2 xx 10^(11 Nm^(-2) , the coefficient of linear expansion for steel = 1.1 xx 10^(-5)//.^(@)CC^(-1) ]

A steel wire of length 20 cm and uniform cross-sectional 1 mm^(2) is tied rigidly at both the ends. The temperature of the wire is altered from 40^(@)C to 20^(@)C . Coefficient of linear expansion of steel is alpha = 1.1 xx 10^(-5) .^(@)C^(-1) and Y for steel is 2.0 xx 10^(11) Nm^(2) , the tension in the wire is

A steel wire is rigidly fixed at both ends its length mass and cross sectional area are 1m, 0.1 kg and 10^(6)m^(2) respectively then the temperature of the wire is lowered by 20^(@)C if the transverse waves are setup by plucking the wire at 0.25m from one end and assuming that wire vibrates with minimum number of loops possible for such a case. Find the frequency of vibration (in Hz). [coefficient of linear expansion of steel =1.21xx10^(-6)//.^(@)C and young's modulus =2xx10^(11)//N//m^(2) ]

A steel wire of length 20 cm and uniform cross-section 1mm^(2) is tied rigidly at both the ends. If the temperature of the wire is altered from 40^(@)C to 20^(@)C , the change in tension. [Given coefficient of linear expansion of steel is 1.1xx10^(5) .^(@)C^(-1) and Young's modulus for steel is 2.0xx10^(11) Nm^(-2) ]

A steel wire of length 20 cm and unifrom crossection mm^(2) is tied rigidly at both the ends. If temperature of the wre is altered from 40^(@)C to 20^(@)C , calcutlate the change in tension. Given coeffeicient of linear expansion of steel is 1.1 xx 10^(-5) .^(@)C^(-1) and Young's modulus for steel is 2.0 xx 10^(11) Nm^(-2) .

A steel wire of uniform cross-sectional area 2mm^(2) is heated upto 50^(@) and clamped rigidly at two ends . If the temperature of wire falls to 30^(@) then change in tension in the wire will be , if coefficient of linear expansion of steel is 1.1 xx 10^(-5)//"^(@)C and young's modulus of elasticity of steel is 2 xx 10^(11) N//m^(2)

A steel wire of length 20 cm and cross - section 1 mm^(2) is tied rigidly at both ends at room temperature 30^(@)C . If the temperature falls 10^(@)C , what will be the change in tension ? Given that Y = 2xx10^(11)N//m^(2) and alpha = 1.1xx10^(-5)//^(@)C

A steel wire fo length 5m and cross-sectional area 2xx10^(-6)m^(2) streches by the same amount as a copper wire of length 4m and cross sectional area of 3xx10^(-6) m^(2) under a given load. The ratio of young's mouduls of steel to that of copper is

ALLEN-WAVES AND OSCILLATIONS-Part-1(Exercise-04)[A]
  1. One end of a long string of linear mass dnesity 8.0xx10^(-3)kgm^(-1) i...

    Text Solution

    |

  2. A uniform rope of length 12 mm and mass 6 kg hangs vertically from a r...

    Text Solution

    |

  3. A steel wire of length 1m, mass 0.1kg and uniform cross-sectional area...

    Text Solution

    |

  4. In the arrangement shown in figure, the string has a mass of 4.5 g. Ho...

    Text Solution

    |

  5. Figure shows a string of linear mass density 1.0g cm^(-1) on which a w...

    Text Solution

    |

  6. A string vibrate according to the equation y = 5 sin ((pi x)/(3)) cos ...

    Text Solution

    |

  7. A bat emits ultrasonic sound of frequency 100 kHz in air. If this soun...

    Text Solution

    |

  8. The vibrations of a string of length 60cm fixed at both ends are repre...

    Text Solution

    |

  9. Given below are some functions of x and t to represent the displacemen...

    Text Solution

    |

  10. If the bulk modulus of water is 4000 MPa, what is the speed of sound i...

    Text Solution

    |

  11. A steel rod 100 cm long is clamped at its middle. The fundamental freq...

    Text Solution

    |

  12. Two successive resonance frequencies in an open organ pipe are 1944 Hz...

    Text Solution

    |

  13. A flute which we treat as a pipe open at both ends is 60 cm long. (a) ...

    Text Solution

    |

  14. A string 25cm long and having a mass of 2.5 gm is under tension. A pip...

    Text Solution

    |

  15. Two tuning fork having frequency 300 Hz & 305 Hz produce beat phenomen...

    Text Solution

    |

  16. Two sitar strings A and B playing the note 'Dha' are slightly out of t...

    Text Solution

    |

  17. A source of sound of frequency 256 Hz is moving towards a wall with a ...

    Text Solution

    |

  18. A person going away from a factory on his scooter at a speed of 36 km/...

    Text Solution

    |

  19. A car has two horns having a difference in frequency of 180 Hz. The ca...

    Text Solution

    |

  20. A whistle emitting a sound of frequency 440 Hz is tied to string of 1....

    Text Solution

    |