Home
Class 12
PHYSICS
When a string is divided into three seg...

When a string is divided into three segments of lengths `l_(1),l_(2) and l_(3)` the fundamental frequencies of these three segments are `v_(1), v_(2) and v_(3)` respectively. The original fundamental frequency (v) of the string is

A

`sqrt(v)= sqrt(v_(1))+sqrt(v_(2))+sqrt(v_(3))`

B

`v= v_(1) + v_(2)+v_(3)`

C

`1/v=1/v_(1) + 1/v_(2)+1/v_(3)`

D

`1/sqrt(v)= 1/sqrt(v_(1))+1/sqrt(v_(2))+1/sqrt(v_(3))`

Text Solution

Verified by Experts

The correct Answer is:
c
The fundamental frequency of string
`v=1/(2l)sqrt(T/m)`
`therefore v_(1)l_(1)=v_(2)l_(2)=v_(3)l_(3)=k ... (i) `
Form Eq. (i), `l_(1)=k/v_(1), l_(2)=k/v_(2), l_(3)=k/v_(3)`
Original length, `l=k/v`
Here, `l=l_(1)+L_(2)+l_(3)`
`k/v=k/v_(1)+k/v_(2)+k/v_(3)`
`rArr 1/v=1/v_(1)+1/v_(2)+1/v_(3)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STATIONARY WAVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|27 Videos

  • STATIONARY WAVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|28 Videos

  • STATIONARY WAVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|28 Videos

  • SEMICONDUCTORS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|25 Videos

  • SURFACE TENSION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|15 Videos

Similar Questions

Explore conceptually related problems

If n_(1), n_(2 ) "and" n_(3) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

If f_(1) and f_(2) be the fundamental frequencies of the two segments into which a stretched string is divided by means of a bridge , then find the original fundamental frequency f of the complete string.

Knowledge Check

  • When a string is divided into three segments of length l_1,l_2 and l_3 the fundamental frequencies of these three segments are f_1,f_2 and f_3 respectively. The original fundamental frequency f of the string is

    A
    `(1)/(sqrtf)=(1)/(sqrt(f_1))+(1)/(sqrt(f_2))+(1)/(sqrt(f_3))`
    B
    `sqrtf=sqrtf_1+sqrtf_2+sqrtf_3`
    C
    `f=f_1+f_2+f_3`
    D
    `(1)/(f)=(1)/(f_1)+(1)/(f_2)+(1)/(f_3)`

  • When a string is divided into three segments of length l_1 , l_2 and l_3 , the fundamental frequency (v) of the string is

    A
    `(1)/(v)=(1)/(v_1) + (1)/(v_2) + (1)/(v_3)`
    B
    `(1)/(sqrt(v))=(1)/(sqrt(v_1)) + (1)/(sqrt(v_2)) + (1)/(sqrt(v_3))`
    C
    `sqrt(v)=sqrt(v_1) + sqrt(v_2)+sqrt(v_3)`
    D
    `v=v_1+v_2+v_3`

  • If n_1,n_2 and n_3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

    A
    `(1)/(n)=(1)/(n_1)+(1)/(n_2)+(1)/(n_3)`
    B
    `(1)/(sqrtn)=(1)/(sqrtn_1)+(1)/(sqrtn_2)+(1)/(sqrtn_3)`
    C
    `sqrtn=sqrtn_1+sqrtn_2+sqrtn_3`
    D
    `n=n_1+n_2+n_3``

    • Similar Questions

    Explore conceptually related problems

    If n_1 , n_2 and n_3 are the fundamental frequencies of three segments into which a string is divided , then the original fundamental frequency n of the string is given by

    A string of length l is divided into four segments of fundamental frequencies f_(1), f_(2), f_(3), f_(4) respectively. The original fundamental frequency f of the string is given by

    A string is cut into three parts, having fundamental frequencies n_(1), n_(2) and n_(3) respectively, Then original fundamental frequency 'n' related by the expression as:

    If v_(1) , v_(2) and v_(3) are the fundamental frequencies of three segments of stretched string , then the fundamental frequency of the overall string is

    A string is cut into three parts, having fundamental frequencies n_(1),n_(2) and n_(3) respectively. Then original fundamental frequency 'n' related by the expression as (other quantities are identical) :-

    Home
    Profile