At 23^ C, a pipe open at both ends resonates at a frequency of 45… - Vidyadip

MCQ

At $23^{\circ} C$, a pipe open at both ends resonates at a frequency of $450 \,Hz$. At what frequency does the same pipe resonate on a hot day when the speed of sound is $4 \%$ higher than it would be at $23^{\circ} C$ ?

A
$446$
B
$454$
✓
$468$
D
$459$

✓

Answer

Correct option: C.

$468$

c
(c)

For an open end pipe, Frequency, $f=\frac{v}{\lambda}=\frac{n v}{2 L}$

$\Rightarrow \quad L=\frac{n v}{2 f}$

As, length of tube remains same in both cases.

$\text { So, } L=\frac{n v_1}{2 f_1}=\frac{n v_2}{2 f_2}$

$\Rightarrow f_2=\frac{v_2}{v_1} \cdot f_1$

Here, $v_2=1.04 v_1$ and $f_1=450 \,Hz$

So, $f_2=\frac{1.04 v_1}{v_1} \times 450$

$=1.04 \times 450$

$=468 \,Hz$

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