Question

Air is blown at the mouth of a tube (Length $25cm$ and diameter $3cm$) closed at one end. Velocity of sound is $330m/s$. the sound which is produced will correspond to the frequencies :

• A. $330Hz$
• B. Combination of frequencies $330,660,990,120,1650Hz$
• C. Combination of frequencies $330,990,1650,2310,Hz$
• D. Combination of frequencies $300,900,1500,2100,Hz$

Answer 1

The correct option is C Combination of frequencies $330,990,1650,2310,Hz$

Given - $l=25cm=0.25m,v=330m/s$ ,

fundamental frequency of a closed organ pipe is given by ,

${\nu }_1=v/4l=330/(4\times 0.25)=330m/s$ ,

frequency of nth normal mode of vibration of closed organ pipe is given by ,

${\nu }_n=(2n-1){\nu }_1$ , $n=1,2,\mathrm{3............}$ ,

therefore first frequency for $n=1$, ${\nu }_1={\nu }_1=330Hz$ ,

second frequency for $n=2$, ${\nu }_2=3{\nu }_1=990Hz$ ,

third frequency for $n=3$, ${\nu }_3=5{\nu }_1=1650Hz$ ,

fourth frequency for $n=4$, ${\nu }_4=7{\nu }_1=2310Hz$