Request a call back

The frequency 'n' of vibration of stretched string depends on its length 'L' its mass per unit length 'm' and the tension 'T' in the string obtain dimensionally an expression for frequency 'n'.

Frequency is denoted by 'n'

let us consider

n= klxTymz ...(1)

Writing dimension for each quantity,
n → [M0L0-1]
l→ [M0L1T0]
T→[M1L1T-2]
m→[M1L-1T0]

Substituting dimensions in equation (1),
[M0L0T-1] = k[M0L1T0]x [M1L1T-2]y [M1L-1T0]z

[M0L0T-1] = k [My+z Lx+y-z T-2y] ...(2)

From (2),
y+z = 0
x+y-z =0
-2y = -1  ....(3)

Solving equations (3) simultanously we get,

x = -1, y = 1/2 and z = -1/2

Substituting these value of x,y and z in equation (1),

n= kl-1T1/2m-1/2

This is the formula for frequency of vibration for stretched string.

Answered by Shiwani Sawant | 06 Aug, 2018, 12:18: PM

## Concept Videos

CBSE 11-science - Physics
Asked by snehasahu824 | 03 Mar, 2020, 10:06: AM
CBSE 11-science - Physics
Asked by devvratagrahari | 02 Dec, 2019, 06:44: AM
CBSE 11-science - Physics
Asked by SELVA | 06 Jul, 2019, 03:25: PM
CBSE 11-science - Physics
Asked by Vidushi412 | 14 Jan, 2019, 09:43: PM
CBSE 11-science - Physics
CBSE 11-science - Physics
Asked by Topperlearning User | 15 May, 2015, 10:54: AM