Question

In a closed organ pipe the fundamental frequency is n. what will be the ratio of frequencies of the next three overtones?

• A. $2:3:4$
• B. $3:4:5$
• C. $3:7:11$
• D. $3:5:7$

Answer 1

The correct option is D $3:5:7$

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

$n_x=(2x-1)n$ , $x=1,2,\mathrm{3............}$ ,

it is $(x-1)th$ overtone ,

given that fundamental frequency is $n_1=n$ ,

therefore , first overtone frequency for $x=2$, $n_2=3n$ ,

second overtone frequency for $x=3$, $n_3=5n$ ,

third overtone frequency for $x=4$, $n_4=7n$ ,

hence ratio of next three fequencies is ,

$n_2:n_3:n_4=3:5:7$