Question

A pipe $20cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5Hz$ ?(sound velocity in air $=330m/s)$

Answer 1

Step 1: Draw a rough diagram.



Step 2: Find harmonic.

Given: $L=20cm=0.2m,\nu =1237.5Hz,v=330m/s.$

$L=\frac{\lambda }{4}$ or $\lambda =4L$

${}^v\text{fundamental}=\frac{v}{4L}$

${}^v\text{fundamental}=\frac{330}{4\times 0.2}$

$=412.5Hz$

${\nu }_{given}=1237.5Hz$

$\frac{{\nu }_{given}}{{\nu }_{fundamental}}=\frac{1237.5}{412.5}=\frac{3}{1}$

So, $3^{rd}$ harmonic of pipe is formed by $1237.5Hz$ frequency.

Final Answer: $3^{rd}$ harmonic