Home
Class 11
PHYSICS
If the tension and diameter of a sonomet...

If the tension and diameter of a sonometer wire of fun-damental frequency n are doubled and the density halved, then its fundamental frequency will become

A

`(n)/(4)`

B

`sqrt(2)` n

C

n

D

`(n)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Mass per unit length of a wire ` m = pi r^(2) rho `
[r = radius, `rho` density of the material]
` :.` fundamental frequency , n ` = (1)/(2l) sqrt((T)/(m)) = (1)/(2l) sqrt((T)/(pi rho))`
`:.` In this case, ofter changing tension and density of sonometer wire, the frequency is
`n^(.) = (1)/(2l(2pi)) sqrt((2T)/(pi((rho)/(2))))=(1)/(4lr) sqrt((4T)/(pi rho))`
` = (1)/(2lr)sqrt((T)/(pi rho)) = n`
[ iIf diameter is doubled radius is also doubled]
`:.` Fundamental frequency remains the same.
Promotional Banner

Topper's Solved these Questions

  • SUPERPOSITION OF WAVES

    CHHAYA PUBLICATION|Exercise Examination archive with solutions (WBJEE)|5 Videos

  • SUPERPOSITION OF WAVES

    CHHAYA PUBLICATION|Exercise Examination archive with solutions (ALEEE)|1 Videos

  • SUPERPOSITION OF WAVES

    CHHAYA PUBLICATION|Exercise Entrance Corner (Integer answer type)|3 Videos

  • STATICS

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|3 Videos

  • THERMOMETRY

    CHHAYA PUBLICATION|Exercise EXAMINATION ARCHIEVE - WBJEE|1 Videos

Similar Questions

Explore conceptually related problems

If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and the density halved , then its fundamental frequency will become

show that the fundamental frequency of an open pipe is double the fundamental frequency of a closed pipe of the same length .

Two open organ pipes of fundamental frequencies n_(1) and n_(2) are joined in series. The fundamental frequency of the new pipe so obtained will be

The frequency of the fundamental emitted from a taut sonometer wire is 250 s^(-1) . Its length is doubled and the tension is increased in such a way that the fundamental frequency remains the same . Obtain the relation between the new and the original tensions .

Two stretched wires made of the same material have lengths, diameters and tensions, each in the ratio 1 : 2 . The first wire emits a fundamental tone of frequency 200 Hz . What is the funcamental frequency of the 2nd wire ?

The ratios of lengths, diameters and masses suspended from the free ends of two sonometer wires of the same meterial are 2 : 3 , 2 : 3 and 1 , 4 , respectively. What is the ratio of their fundamental frequencies ?

Angular momentum of a particle revolving with uniform speed is L. If the frequency of the particle is doubled and its kinetic energy is halved then its angular momentum becomes