An open organ pipe of length $l$ is sounded together with another open organ pipe of length $(l+l_1)$ in their fundamental modes. Speed of sound in air is $V$. The beat frequency heard will be $(l_1 \ll l)$

  • A
    $\frac{V l_1^2}{2 l}$
  • B
    $\frac{V l_1}{2 l^2}$
  • C
    $\frac{V l_1}{4 l^2}$
  • D
    $\frac{V l^2}{2 l_1}$

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For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz, 595 \, Hz,$ and $765 \, Hz$ respectively. Taking the speed of sound in air to be $340 \, m/s$,the fundamental frequency of the pipe (in $Hz$) is:

Two closed pipes produce $10$ beats per second when emitting their fundamental notes. If their lengths are in the ratio of $25 : 26$,then their fundamental frequencies in $Hz$ are:

$A$ student is experimenting with a resonance tube apparatus in a Physics lab to find the speed of sound at room temperature. He obtained the first two resonating lengths of the air column as $17 \, cm$ and $51 \, cm$,using a tuning fork of frequency $512 \, Hz$. Find the speed of sound at room temperature in $m/s$.

In a physics lab,a student is performing an experiment with a resonance tube to find the speed of sound and its end correction. For this,he used a resonance tube of length $120 \ cm$. When the length of the air column in the tube is $16 \ cm$ and $50 \ cm$,he obtains the $I$ and $II$ resonance respectively,while a tuning fork of frequency $500 \ Hz$ is sounded just above the tube. Match the parameters in List-$I$ with their suitable values in List-$II$.
List-$I$ List-$II$
$A$. Wavelength of sound $(cm)$ $p$. $1$
$B$. Height of liquid column at $II$ resonance $(cm)$ $q$. $2$
$C$. Speed of sound $(m/s)$ $r$. $340$
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