Step 1: Write the formula for frequency in an open pipe
The frequency of the
nth harmonic in an open organ pipe is:
f0=‌Step 2: Find the frequency for the 3rd harmonic in the open pipe
For the third harmonic,
n=3 :
f0′=‌Step 3: Write the formula for frequency in a closed pipe
The frequency of the
nth harmonic in a closed pipe is:
fc=‌Step 4: Find the frequency for the 5th harmonic in the closed pipe
For the fifth harmonic,
n=5 :
fc′=‌Step 5: Write the ratio of the two frequencies
We want to find the ratio
‌.
‌=‌Step 6: Simplify the ratio
First, simplify by dividing:
‌×‌=‌Step 7: Use the ratio of lengths
It is given that the ratio of lengths of the open and closed pipes is
2:3, so
‌=‌.
Step 8: Substitute the value for
‌‌×‌=‌×‌=‌×‌=‌=‌Step 9: State the final ratio
The ratio of the frequencies is
9:5.