Question

Some of the frequencies of tones produced by an organ pipe are $220,440,550,660Hz$. Find the effective length of the pipe. (take, the speed of sound in air$=330m/s$)

• A. $1.8m$
• B. $1.7m$
• C. $1.5m$
• D. $1.2m$

Answer 1

The correct option is C

$1.5m$

Step 1: Given Data:

Frequencies produced by an organ pipe$=220,440,550,660Hz$

The speed of sound in air$=330m/s$

Step 2: Formula Used:

$\begin{array}{rcl}Lengthofpipe\left(l\right)& =& \frac{1}{2}\frac{Speedofair\left(v\right)}{fundamentalfrequency\left(v_0\right)}\end{array}$

Step 3: Calculating the length of the pipe:

As we can see these are all the multiples of $110$

Therefore, the fundamental frequency is $110$

Now calculating the length of the pipe,

$\begin{array}{rcl}Lengthofpipe\left(l\right)& =& \frac{1}{2}\frac{Speedofair\left(v\right)}{fundamentalfrequency\left(v_0\right)}\\ & =& \frac{1}{2}·\frac{330}{110}\\ & =& 1.5m\end{array}$

Thus, the effective length of the pipe is $1.5m$

Hence option (c) is correct.