Question
Physics Question on Electromagnetic waves
Two stretched strings of same material are vibrating under same tension in fundamental mode. The ratio of their frequencies is 1 : 2 and ratio of the length of the vibrating segments is 1 : 4. Then the ratio of the radii of the strings is
A
2:01
B
4:01
C
3:02
D
8:01
Answer
8:01
Explanation
Solution
\hspace15mm n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^2 d}}
where l is length, T is tension, r is radius and dis density.
Given, \hspace20mm \frac{n_1}{n_2}= \frac{1}{2},\frac{l_1}{l_2} = \frac{1}{4}
\therefore \hspace25mm \frac{n_1}{n_2}=\frac{l_2}{l_1} \sqrt{\frac{r^2_2}{r^2_1}}
\Rightarrow \hspace20mm \bigg(\frac{n_1l_1 }{n_2 l_2}\bigg)^2 =\frac{r^2_2}{r^2_1}
\Rightarrow \hspace30mm \frac{r_1}{r_2} = \frac{n_1l_1 }{n_2 l_2} = 2 \times 4 = 8:1