Question

For a resonance tube the air columns for the first and the second resonance differ in length by $31.5cm$. The wavelength of the sound wave is (in cm)

• A. $126.0$
• B. $63.0$
• C. $31.5$
• D. $252.0$

Answer 1

Answer: (B)

$63.0$

The length of the resonant air column in tube is

$l=\frac{n\lambda }{2}$

For n = 1,

$l_1=\frac{\lambda }{2}$

For n = 2,

$l_2=\frac{2\lambda }{2}=\lambda$

Hence,

$l_2-l_1=\lambda -\frac{\lambda }{2}$

$l_2-l_1=\frac{\lambda }{2}$

$\lambda =2(l_2-l_1)$

$\lambda =2\left(31.5\right)$ ....................(given)

$\lambda =63cm$