If the vibration of a string are to be increased by a factor of 2. Then tension in the string must be made :

Question

If the vibration of a string are to be increased by a factor of 2. Then tension in the string must be made : (A) 8 times (B) 4 times (C) 1/3 times (D) half times

Tardigrade Admin · Accepted Answer

Here, initial vibration n1=n Final vibration n2=2n Initial tension T=T The vibration of frequency of string is n=(1/2l)(√T/m) propto √T Hence, (n1/n2)=(√T1/T2) or (n/2n)(√T1/T2) or (T1/T2)=(1/4) or T2=4T1

Q. If the vibration of a string are to be increased by a factor of 2. Then tension in the string must be made :

8 times

4 times

1/3 times

half times

Here, initial vibration n1​=n Final vibration n2​=2n Initial tension T=T The vibration of frequency of string is n=2l1​mT​​∝T​ Hence, n2​n1​​=T2​T1​​​ or 2nn​T2​T1​​​ or T2​T1​​=41​ or T2​=4T1​