Wave Mechanics Question 644
Question: If the length of a stretched string is shortened by 40% and the tension increased by 44% then the ratio of the final and initial fundamental frequencies is
Options:
A) 3 : 4
B) 4 : 3
C) 1 : 3
D) 2 : 1
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ n=\frac{1}{2\ell }\sqrt{\frac{T}{m}}\
Therefore \frac{n _{2}}{n _{1}}=\frac{{\ell _{1}}}{{\ell _{2}}}\sqrt{\frac{T _{2}}{T _{1}}} $
$ =\frac{{\ell _{1}}}{[ {\ell _{1}}-\frac{40}{100}{\ell _{1}} ]}\frac{\sqrt{T _{1}+( \frac{44}{100} )}T _{1}}{T _{1}} $
$ =\frac{100}{60}\times \frac{12}{10}=2:1 $
BETA
