First slide

Beats

Question

Length of a closed pipe is 75 cm. First overtone of this closed pipe beats with the first over tone of an open pipe with a beat frequency of 5 Hz. If velocity of sound in air is 330 Hz, what is the length of the open pipe ?

Moderate

A

96.5 cm
B

98.5 cm
C

101.5 cm
D

both 2 and 3 are right.

Solution

First overtone of closed pipe = ${(f_{1})}_{C}$
First overtone of open pipe = ${(f_{1})}_{0}$
$\begin{array}{l} {(f_{1})}_{C} = 3 . \frac{V}{4 l_{C}} = 3 \times \frac{330}{4 \times 0 .75} Hz = 330 Hz \\ {(f_{1})}_{0} = 4 . \frac{V}{4 l_{0}} = \frac{330}{l_{0}} . Hz \end{array}$
$\begin{array}{l} Now \frac{330}{l_{0}} - 330 = 5 \Rightarrow l_{0} = 0 .985 m = 98 .5 cm . \\ Again, 330 - \frac{330}{l_{0}} = 5 \Rightarrow l_{0} = 1 .015 m = 101 .5 cm . \end{array}$

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