Question

When an 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
• D. 300 Hz

Answer 1

The correct option is D 300 Hz

Let the length of the pipe be $L$ and speed of sound in air be $v$.

Third over tone $(n=4)$ frequency of closed pipe ${\nu }^{\prime }=\frac{(2\times 4-1)v}{4L}$

$⟹$ ${\nu }^{\prime }=\frac{7v}{4L}$

Second overtone frequency of open pipe $(n=3)$, $\nu =\frac{3v}{2L}$

But, ${\nu }^{\prime }-\nu =150$

$\therefore$ $\frac{7v}{4L}-\frac{3v}{2L}=150$

Or $\frac{1v}{4L}=150$

we get $\frac{v}{2L}=300$ Hz

Thus fundamental frequency of open pipe ${\nu }_f=\frac{v}{2L}=300$ Hz