Question

If the length of a stretched
string is shortened by 40 %
and the tension is increased
by 44 % then the ratio of the
final and initial -
fundamental frequencies is
​

Answer 1

Question: If the length of a stretched  string is shortened by 40 %  and the tension is increased  by 44 % then the ratio of the  final and initial -  fundamental frequencies is

Solution: $2:1$

Step by step explanation:

$n=\frac{1}{2l} \sqrt{\frac{T}{m} } \\\frac{n_2}{n_1} = \frac{l_1}{l_2} \sqrt{\frac{T_2}{T_1} } \\= \frac{l_1}{[l_1-\frac{40}{100}l_1] } \sqrt{(\frac{T_1+\frac{4}{100}T_1 }{T_1} } )\\= \frac{100}{60} \times\frac{12}{10} = 2:1$