Question

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

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

Answer 1

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

Frequency of $x^{th}$ normal mode of vibration of closed organ pipe is given by, $n_x=(2x-1)n,x=1,2,\mathrm{3...}$

Given the 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 frequencies is , $n_2:n_3:n_4=3:5:7$

Hence, option (d) is the correct answer.