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Home  ›  Youngs modulus of a rock specimen of density 2.7 gm/cc is 9.72 megabar. The longitudinal wave velocity (in km/s) in the rock is

CSIR-NET 2017 DEC(46)

21 comments

CSIR-NET

46. Youngs modulus of a rock specimen of density 2.7 gm/cc is 9.72 megabar. The longitudinal wave velocity (in km/s) in the rock is 

1. 4.8
2. 5.2
3. 6.0
4. 7.2

Solution:
Using Young's modulus we can calculate the Bulk modulus and rigidity modulus and then finally we can calculate the P-wave velocity (Please check it comment section).  In this case I'm not getting the answer.

If I calculate the One-dimensional Wave velocity, 

Wave Velocity  (V) = √(E/ ρ) -------------------(1)

E-Young's modulus = 9.72 megabar

                            = 9.72 *106 bar

                            =9.72* 1011 pascal

                           =972* 109 pascal

Density = 2.7 gm/cc

              =2700 kg/m3

Above valuses substitute in eq(1)

V = √ (972*109 /2700)

V = √ (36*107)

V=6000 m/s

V = 6 km/s

( I am getting one zero extra. If anyone knows please correct this problem)



Another solution:

Thanks to Rohit Jha,

 

Using Inverse Gardner equation from density in $\rho$ gm/cc and velocity of the longitudinal wave is in m/s


Given values,


$\rho$=2.7 gm/cc


What is $V_p$ is in m/s?

 

$V_p=108 \rho^4$

 

$V_p=108 (2.7)^4$

 

$V_p=5739.56 m/s$

 

Therefore $V_p=5.739 km/s$



Reference :Gardner's equation - SubSurfWiki



Youngs modulus of a rock specimen of density 2.7 gm/cc is 9.72 megabar. The longitudinal wave velocity (in km/s) in the rock is

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21 comments

  1. భూ-భౌతికం5 January 2018 at 22:53

    Same problem :(

    ReplyDelete
  2. Sivaiah B12 June 2018 at 23:01

    Super Brother. You are doing Good Job really, Keep it up.

    ReplyDelete
  3. Unknown14 September 2018 at 00:25

    Given youngs modulus not bulk .. still nice work keep it up .

    ReplyDelete
  4. Subh14 September 2018 at 05:10

    It's given young's modulus not bulk modulus sir.By putting Young's modulus formula it's not giving any of the given value. Please help me out for this. Thank you

    ReplyDelete
    Replies
    1. GPSURYA17 September 2018 at 05:52

      very nice doubt subh..

      Delete
    2. GPSURYA17 September 2018 at 05:59

      use K= E/3(1-2v),
      K bulk modulus
      E young's modulus
      v poisson's ratio (0.25 for ideal case)

      for this values

      k= 648*10^9

      submit this value in Vp^2= (k/p)

      p- density

      Answer for this: 4.8 km/s (please check it once)

      Delete
    3. GPSURYA17 September 2018 at 06:00

      Thank you subh...

      Delete
    4. Unknown29 March 2020 at 06:13

      no answer is 6.0

      Delete
    5. GPSURYA29 March 2020 at 07:52

      If you like this blog, please follow me.. Please share your solution..

      Delete
  5. Viswa4 December 2019 at 03:05

    Very good job. Thank you for solution.
    But

    VP = √ (36*107)

    VP=6000 m/s.... How is it come.

    VP = √ (36*107) = 6000*√ (10).......Please check it.

    ReplyDelete
    Replies
    1. GPSURYA4 December 2019 at 10:10

      Please check above comment which I was posted , in this first we have to calculate bulk modulus using Young's modulus, then we will calculate the longitudinal velocity ...

      Delete
  6. Unknown4 September 2020 at 21:33

    First we need to calculate bulk modulus using young's modulus, then we need to calculate shear modulus using bulk modulus, then substitute in the Vp formula and the answer will come 20.7 km/sec....need to change bar into pascal and gm/cc into kg/m3

    ReplyDelete
    Replies
    1. GPSURYA4 September 2020 at 23:15

      ok i will check it...

      Delete
    2. GPSURYA10 October 2020 at 20:24

      But one more thing we have to consider, no where in the earth the the P-wave velocity is 20km/s.

      Delete
    3. Shivjay Volvoikar10 February 2023 at 02:30

      Sir, what he said is correct. We have to solve it like that. But i am getting 2.0 km/sec

      Delete
  7. zeliz10 October 2020 at 08:56

    why havent you considered the rigidity modulus here

    ReplyDelete
  8. Rohit Jha6 July 2021 at 04:18

    Use Gardner equation
    Vp= 108*(density)^4 m/sec

    Vp= 108*(2.7)^4
    Vp= 5739.36 m/s
    Vp= 5.739 km/s
    Vp=6km/s(Approx)

    ReplyDelete
    Replies
    1. GPSURYA12 July 2021 at 04:09

      Thank you Rohit. Please send me name of the reference text book.

      Delete
  9. Rohit Jha16 July 2021 at 21:18

    https://www.subsurfwiki.org/wiki/Gardner%27s_equation#:~:text=Gardner's%20equation%20is%20an%20empirical,when%20performing%20a%20well%20tie).

    ReplyDelete
    Replies
    1. GPSURYA17 July 2021 at 10:01

      Thank you so much Rohit. So In this case we won't consider the Young's modulus right. I will update your solution also.

      Delete

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