Question

In a closed end pipe of length 105 cm, standing waves are set up corresponding to the third overtone. What distance from the closed end, amongst the following, is a pressure Node?

• A. 20 cm
• B. 60 cm
• C. 85 cm
• D. 45 cm

Answer 1

The correct option is D 45 cm

For a closed organ pipe,

$\lambda =\frac{4L}{2m+1}$,

here, $m=0,1,2,3,...$ for fundamental tone, first overtone, second overtone and third overtone and so on ...

For third overtone, $\lambda =\frac{4\times 105}{2\times 3+1}=60cm$

Pressure Nodes from the close end will form at, $\lambda /4,3\lambda /4,5\lambda /4..etc$
Pressure Nodes from the close end will form at, $15cm,45cm,75cm,105cm$