TG EAMCET 2 May 2025 Shift 2 Paper

Step 1: Write the formula for frequency in an open pipe
The frequency of the nth harmonic in an open organ pipe is:
f0=‌

nv

2l0

Step 2: Find the frequency for the 3rd harmonic in the open pipe
For the third harmonic, n=3 :
f0′=‌

3v

2l0

Step 3: Write the formula for frequency in a closed pipe
The frequency of the nth harmonic in a closed pipe is:
fc=‌

nv

4lc

Step 4: Find the frequency for the 5th harmonic in the closed pipe
For the fifth harmonic, n=5 :
fc′=‌

5v

4lc

Step 5: Write the ratio of the two frequencies
We want to find the ratio ‌

f0′

fc′

.
‌

f0′

fc′

=‌

‌ 3v 2l0

5v 4lc

Step 6: Simplify the ratio
First, simplify by dividing:
‌

3v

2l0

×‌

4lc

5v

=‌

12lc

10l0

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 ‌

l0

lc

=‌

2

3

.
Step 8: Substitute the value for ‌

l0

lc

‌

12

10

×‌

1

l0 lc

=‌

12

10

×‌

1

2 3

=‌

12

10

×‌

3

2

=‌

36

20

=‌

9

5

Step 9: State the final ratio
The ratio of the frequencies is 9:5.