Home
Class 12
PHYSICS
A stationary wave y=0.4"sin"(2pi)/40 cos...

A stationary wave `y=0.4"sin"(2pi)/40 cos 100pit` is produced in string fixced of both ends. The minimum possible length of the string is given by

A

`10m`

B

`20sqrt(2)m`

C

`20m`

D

`28m`

Text Solution

Verified by Experts

The correct Answer is:
C
According to the question statioinary wave is
`y=0.4 "sin"(2pix)/40cos 100pit`
As string is fixed at both the ends where nodes are formed. Standard equation of stationary wave is given by
`y=2a"sin"(2pix)/(lamda)"cos"(2pivt)/(lamda)`
Compare them `(2pix)/(lamda)=(2pix)/40`
Or `lamda=40m`
`:.` Distance between two nodes `=(lamda)/2`
`:.` Minimum length of rod `=(lamda)/2`
`=40/2=20m`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 07

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 1( PHYSICS & CHEMISTRY)|50 Videos

  • PRACTICE SET 09

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 1 (PHYSICS & CHEMISTRY)|50 Videos

Similar Questions

Explore conceptually related problems

A standing wave with a number of loops is produced in a stringe fiex at both ends. In this case

The wave-function for a certain standing wave on a string fixed at both ends is y(x,t) = 0.5 sin (0.025pix) cos500t where x and y are in centimeters and t is seconds. The shortest possible length of the string is :

The transverse displacement of a string fixed at both ends is given by y=0.06sin((2pix)/(3))cos(100pit) where x and y are in metres and t is in seconds. The length of the string is 1.5 m and its mass is 3.0xx10^(-2)kg . What is the tension in the string?

A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm respectively. The minimum possible length of the string is:

A standing wave is produced on a string on a string clamped at one end and free at the other. The length of the string

The equation of a stationary wave is y=4sin((pi x)/(5))cos(100 pi t) .The wave is formed using a string of length 20cm .The 2^(nd) and 3^(rd) antinodes are located at positions (in cm) ?

A string 1 m long is fixed at one end. The other end is moved up and down with frequency 20 Hz. Due to this, a stationary wave with four complete loops, gets produced on the string. Find the speed of the progressive wave which produces the stationary wave. [Note: Remember that the moving end is a antinode.]

For the stationary wave y=4sin((pix)/(15))cos(96pit) , the distance between a node and the next antinode is

The displacement of a string is given by y(x,t)=0.06sin(2pix//3)cos(120pit) where x and y are in m and t in s. The lengthe of the string is 1.5m and its mass is 3.0xx10^(-2)kg.

The transvers displacement of a string (clamped at its both ends) is given by y(x,t) = 0.06 sin ((2pi)/(3)s) cos (120 pit) Where x and y are in m and t in s . The length of the string 1.5 m and its mass is 3.0 xx 10^(-2) kg . Answer the following : (a) Does the funcation represent a travelling wave or a stational wave ? (b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength. Frequency and speed of each wave ? Datermine the tension in the string.

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 08-PAPER 1 OBJECTIVE TYPE
  1. A bullet of mass 10 g moving with 300m//s hits a block of ice of mass ...

    Text Solution

    |

  2. A North pole of 40A-m is palced 20 cm apart from a South pole of 80A-m...

    Text Solution

    |

  3. Wires A and B are made from the same material. A has twice the diamete...

    Text Solution

    |

  4. A point source of light is placed 4 m below the surface of water of re...

    Text Solution

    |

  5. A 100V, aC source of frequency of 500Hz is connected to an L-C-LR circ...

    Text Solution

    |

  6. In an ideal transformer, the voltage and current in the primary are 20...

    Text Solution

    |

  7. The energy difference between the first two levels of hydrogen atom is...

    Text Solution

    |

  8. A steel wire 0.5 m long has a total mass of 0.02 kg and is stretched w...

    Text Solution

    |

  9. Energy E of a hydrogen atom with principle quantum number n is given b...

    Text Solution

    |

  10. A convex lens has its radi of curvature equal. The focal length of the...

    Text Solution

    |

  11. An organ pipe closed at one end has fundamental frequency of 1500hz. T...

    Text Solution

    |

  12. Assuming that the silicon diode (having negligible resistance) the cur...

    Text Solution

    |

  13. A sinusoidal voltage of rms value 100V is connected to an ideal functi...

    Text Solution

    |

  14. A stationary wave y=0.4"sin"(2pi)/40 cos 100pit is produced in string ...

    Text Solution

    |

  15. A sonometer wire resonates with a given tuning fork forming a standing...

    Text Solution

    |

  16. If a ladder weighting 250 N is placed against a smooth vertical wall h...

    Text Solution

    |

  17. Four waves A, B, C, D of frequencies 6 MHz. 8 MHz, 10 MHz and 4 MHz re...

    Text Solution

    |

  18. Two identical capacitors, have the same capacitance C. One of them is ...

    Text Solution

    |

  19. For a certain metal, incident frequency v is five times of threshold f...

    Text Solution

    |

  20. A simple pendulum is set into vibrations. The bob of the pendulum come...

    Text Solution

    |