A uniform wire of length L and mass M is stretched between two fixed points,keeping a tension F. A sound of frequency u is impressed on it. Then the maximum vibrational energy is existing in the wire when u=

Asked by Anil | 10th May, 2017, 09:00: PM

Expert Answer:

The frequency of the wire depends on the length of the string (L), tension (F) and the mass per unit length of the wire (m = M/L)
Let Abegin mathsize 12px style proportional to end styleLaFbmc ........ (Equation 1)
Writing the dimensions of each in the above equation, we get
[M0L0T-1] = La [M1L1T-2]b [M0L-1]c
                 = Mb+cLa+b-cT-2b
Here, b + c = 0 ; 
  a + b − c = 0  and
   − 2b = − 1
On solving, we get
a = −1 , b = 1/2 and c = −1/2
Substituting these values in equation (1), we get
begin mathsize 12px style straight A space equals space straight k space straight L to the power of negative 1 end exponent straight F to the power of 1 divided by 2 end exponent straight m to the power of negative 1 divided by 2 end exponent
space space space space equals space straight k 1 over straight L square root of straight F over straight m end root
or space straight A space equals space straight k 1 over straight L square root of fraction numerator straight F over denominator left parenthesis straight M divided by straight L right parenthesis end fraction end root
or space straight A space equals space space straight k square root of straight F over ML end root
Experimentally space straight k space equals space 1 divided by 2
therefore straight A space equals space space 1 half square root of straight F over ML end root end style
 
 

Answered by Yashvanti Jain | 11th May, 2017, 04:31: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.