(B) Let $x$ be the end correction.For the fundamental mode (first resonance),the length of the air column is $l_1 = 0.1 \ m$. The resonance condition

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(B) Let $x$ be the end correction.For the fundamental mode (first resonance),the length of the air column is $l_1 = 0.1 \ m$. The resonance condition is given by $f = \frac{v}{4(l_1 + x)}$.For the first overtone (second resonance),the length of the air column is $l_2 = 0.35 \ m$. The resonance condition is given by $f = \frac{3v}{4(l_2 + x)}$.Since the same tuning fork is used,the frequency $f$ remains constant. Therefore,$\frac{v}{4(l_1 + x)} = \frac{3v}{4(l_2 + x)}$.Simplifying the equation: $l_2 + x = 3(l_1 + x)$.Substituting the values: $0.35 + x = 3(0.1 + x)$.$0.35 + x = 0.3 + 3x$.$0.05 = 2x$.$x = 0.025 \ m$.

Class 11 Physics Waves and Sound Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

Medium

In the experiment for the determination of the speed of sound in air using the resonance column method,the length of the air column that resonates in the fundamental mode with a tuning fork is $0.1 \ m$. When this length is changed to $0.35 \ m$,the same tuning fork resonates with the first overtone. Calculate the end correction in $m$.

IIT 2003 All IIT

A
$0.012$
B
$0.025$
C
$0.05$
D
$0.024$

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Waves and Sound

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Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

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The lengths of the two organ pipes open at both ends are $L$ and $(L+L_1)$. If they are sounded together,the beat frequency will be ($v=$ velocity of sound in air).

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