Question

A set of open-ended pipes with waves vibrating inside them as per shown in above figure.

Identify the pipe containing waves with the highest frequency?

• A. $A$
• B. $B$
• C. $C$
• D. $D$
• E. $E$

Answer 1

The correct option is E $E$

Let L be the length of organ pipe , and v be the wave speed,

for fig. A ,

$L=2\lambda /2=\lambda$

$\lambda =L$

$frequencyf=v/\lambda =v/L$

for fig. B ,

$L=\lambda /2$

$\lambda =2L$

$frequencyf=v/\lambda =v/2L$

for fig. C ,

$L=2\lambda /3$

$\lambda =3L/2$

$frequencyf=v/\lambda =2v/3L$

for fig. D ,

$L=5\lambda /2$

$\lambda =2L/5$

$frequencyf=v/\lambda =5v/2L$

for fig. E ,

$L=4\lambda$

$\lambda =L/4$

$frequencyf=v/\lambda =4v/L$

It is clear that fig E has maximum frequency.