Question 492: Waves

Question

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.

Accepted Answer

From formula, $$f = {1 \over x}\sqrt {{T \over m}} $$
$$ \Rightarrow {1 \over f} \propto l$$
$$ 	herefore {l_1}:{l_2}:{l_3} = {1 \over {{f_1}}}:{1 \over {{f_2}}}:{1 \over {{f_3}}}$$
=  f
2
f
3
: f
1
f
3
: f
1
f
2
[Given: f
1
: f
2
: f
3
= 1 : 3 : 5]
= 15 : 5 : 3
Therefore the positions of two bridges below the wire are
$${{15 	imes 100} \over {15 + 5 + 3}}cm$$ and $${{15 	imes 100 + 5 	imes 100} \over {15 + 5 + 3}}cm$$
$$ \Rightarrow {{1500} \over {23}}cm,\,\,{{2000} \over {23}}cm$$

Answer

$${{1500} \over {23}}cm,{{500} \over {23}}cm$$

Answer

$${{1500} \over {23}}cm,$$ $${{300} \over {23}}cm$$

Answer

$${{300} \over {23}}cm,{{1500} \over {23}}cm$$

Answer

$${{1500} \over {23}}cm,{{2000} \over {23}}cm$$

Waves

The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.

Choose the correct answer: