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Question
A Kundt's tube apparatus has a copper rod of length 1.0 m clamped at 25 cm from one of the ends. The tube contains air in which the speed of sound is 340 m s−1. The powder collects in heaps separated by a distance of 5.0 cm. Find the speed of sound waves in copper.
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Solution
Given:
Speed of sound in air \[v_{air}\]= 340 ms−1
Velocity of sound in Kundt's tube \[v_{rod}\] = ?
Length at which copper rod is clamped l = 25 cm = 25\[\times {10}^{- 2} \text { m }\]
Distance between the heaps \[∆ l\]= 5 cm =\[5 \times {10}^{- 2} \text { m }\]
\[\frac{v_{rod}}{v_{air}} = \frac{2l}{∆ l}\]
\[ \Rightarrow v_{rod} = \frac{2l}{∆ l} \times v_{air} \]
\[\text { On substituting the respective values in the above equation, we get: }\] \[ v_{rod} = \frac{340 \times 25 \times {10}^{- 2} \times 2}{5 \times {10}^{- 2}}\]
\[ \Rightarrow v_{rod} = 3400 \text { m/s }\]
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