When open pipe is closed from one end then third overtone of clos… - Vidyadip

MCQ

When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by $150 Hz$ than second overtone of open pipe. The fundamental frequency of open end pipe will be

A
$75 Hz$
B
$150 Hz$
C
$225 Hz$
✓
$300 Hz$

✓

Answer

Correct option: D.

$300 Hz$

(d) : Frequency of third overtone in a pipe closed at one end, $n_3=\frac{7 v}{4 L}$
Frequency of second overtone in an open pipe,
$
n_2^{\prime}=\frac{3 v}{2 L}
$
As $n_3-n_2^{\prime}=150 Hz$ (given)
$
\therefore \quad \frac{7 v}{4 L}-\frac{3 v}{2 L}=150 Hz \text { or } \frac{v}{4 L}=150 Hz
$
Fundamental frequency of open pipe,
$
n=\frac{v}{2 L}=\frac{2 v}{4 L}=2 \times 150 Hz =300 Hz
$

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