Question 11: Waves

Question

In a resonance coloum first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obtained at depth.

Accepted Answer

Given, first resonance column at depth, $${l_1} = 24$$ cm
Second resonance column at depth, $${l_2} = 78$$ cm
Third resonance column at depth, $${l_3} = ?$$
As
$${l_1} + x = {\lambda  \over 4} = 24$$ ..... (i)
$${l_2} + x = {{3\lambda } \over 4} = 78$$ ........ (ii)
$${l_3} + x = {{5\lambda } \over 4}$$ ........ (iii)
From Eqs. (i) and (ii),
$$x = {{{l_2} - 3{l_1}} \over 2} = {{78 - 3(24)} \over 2} = 3$$ ....... (iv)
From Eqs. (iii) and (i), $${{{l_3} + x} \over {{l_1} + x}} = 5$$
$${l_3} = 5{l_1} + 5x - x = 5{l_1} + 4x$$
Substituting $$l_1$$ and x value, we get
$${l_3} = 5(24) + 4(3) \Rightarrow {l_3} = 132$$ cm.

Answer

160 m

Answer

132 m

Answer

131 m

Answer

152 m

Waves

In a resonance coloum first and second resonance are obtained at depths 24 cm and 78 cm the third resonance will be obtained at depth.

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