Whatwould be the change in the fundamental frequency of a stringedlnstrument if(i) the length of the string is doubled, (ii) the tension is doubled, (iii) the diameter is doubled ?

Whatwould be the change in the fundamental frequency of a stringedlnst

1.	Whatwould be the change in the fundamental frequency of a stringedlnstrument if(i) the length of the string is doubled, (ii) the tension is doubled, (iii) the diameter is doubled ?
Answer» Answer : (i)Thefrequency is inversely proportional to the length of the string. So , if the length is doubled, the fundamental frequency wouldbe reduced to half . (ii)Frequency is proportional to the square root of the tension. So , if the tension is doubled, the fundamental frequency WOULD be `sqrt(2)` or 1 . 414 times of its INITIAL value . (iii) If the diameter is doubled, the area of CROSS section becomes`2^(2)` or 4 times the initial value.If the materials of the string is the same, the mass per unit length also becomes 4 times its original value.Thefrequency is inversely proportional to the square root of the mass per unit length.So , inthis CASE,the frequency wouldbe `(1)/(sqrt(4))`or`(1)/(2)`times, i.e., half the initial value .