The frequency of the note emitted by a stretched string is 300 Hz. What is the frequency of this note when: 

(a) Length of the wave is reduced by one third without changing tension.

(b) The tension is increased by one-third without changing the length of the wire. 

(Ans: 450 Hz, 346 Hz)



Data Given:


Frequency of note = f = 300 Hz


To Find:


(a) Frequency of note = f₁ = ? {When length of the wave is reduced by one third without changing tension.}

(b) Frequency of note = f₂ = ? {When the tension is increased by one-third without changing the length of the wire. }


Solution:


(a) Frequency of note = f₁ = ? {When length of the wave is reduced by one third without changing tension.}


According to given conditions let original wavelength λ is reduced by 1313 then the new wavelength λ₁ will be 
λ₁ = λ - λ3 = 2λ3

As given there is no change occur in the tension F then the speed will remains constant.

v₁ = v

or

f₁ λ₁ λ

or

f₁ fλλ

putting value of λ₁ = 2λ3

f₁ fλ2λ3

or

f₁ 3f2

putting the value of f = 300 Hz (given)

f₁ 3300Hz2

f₁ = 450 Hz  -----------------Ans.
Hence the new frequency will increase to 450 Hz


(b) Frequency of note = f₂ = ? {When the tension is increased by one-third without changing the length of the wire. }

According to given conditions let the tension F is increased by 13 then the new tension F will be 
F₂ = F + F3 = 4F3

Formula for fundamental frequency 

f = 13L Fm  ----------(1)

and the new frequency after increasing tension F = 4F3


f = 13L Fm

or

f = 13L 4F3m -------(2)

Now dividing equation (2) by (1) we will get

ff = 43

ff = 1.155

or

f 1.155 x f

putting f = 300 Hz (given)

f 1.1547 x 300 Hz

f = 346.41 Hz

or

f = 346 Hz -----------------Ans. (2)



************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK    

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.