Question

Speed of sound in air is 320 m/s. A pipe closed at one ends has a length of 1 m and there is another pipe open at both ends having a length of 1.6 m. Neglecting and corrections, both the air columns in the pipes can resonate for sound of frequency :

• A. 80 Hz
• B. 240 Hz
• C. 320 Hz
• D. 400 Hz

Answer 1

The correct option is D 400 Hz

The closed organ pipe can vibrate at frequency of $f=\frac{v}{\lambda }$

$\frac{{\lambda }_1}{4}=1$ $\Rightarrow f_1=\frac{320}{4}=80Hz$

$\frac{3{\lambda }_2}{4}=1$ $\Rightarrow f_2=\frac{3\times 320}{4}=240Hz$

$\frac{5{\lambda }_3}{4}=1$ $\Rightarrow f_3=\frac{5\times 320}{4}=400Hz$

The open organ pipe can vibrate at frequency of $f=\frac{v}{\lambda }$

$\frac{{\lambda }_1}{2}=1.6$ $\Rightarrow f_1=\frac{320}{3.2}=100Hz$

${\lambda }_2=1.6$ $\Rightarrow f_2=\frac{\times 320}{1.6}=200Hz$

$\frac{3{\lambda }_3}{2}=1.6$ $\Rightarrow f_3=\frac{3\times 320}{3.2\times 2}=300Hz$

$2{\lambda }_2=1.6$ $\Rightarrow f_4=\frac{\times 320}{0.8}=400Hz$

Hence both pipes can vibrate at $400Hz$ frequency