What are the first, second, and third frequencies audible from a 20 cm long organ pipe when (A) only one end is open and when (B) both ends are open. The speed of sound through the air inside the organ pipe is 343m/s
(A) When only one end is open, it is a 'closed' pipe and so we use
Where fn = frequency of nth harmonic (Hz)
n = harmonic number
v = speed of sound inside the pipe (m/s)
L = length of pipe closed at one end (m)
Plugging in the values and solving, we get f1 = 428.75 Hz
f3 = 1286.25 Hz
f5 = 2143.75 Hz
(B) When both ends are open, it is an 'open' pipe and so we use
Plugging in the values and solving, we get f1 = 857.5 Hz
f2 = 1715 Hz
f3= 2572.5 Hz
when one end is open, the pipe is 1/4 *nodd wavelength long.
f*lambda=v
f*4/n * .2=v
solve for f. given, n=1,3,5
both ends open, the pipe is n/2 lambda long, n =1,2,3,
f*2/n
To determine the first, second, and third frequencies audible from an organ pipe, we can use the formula for the frequencies of standing waves in a closed-end or open-end pipe.
(A) When only one end of the organ pipe is open:
The first frequency (fundamental frequency) for a closed-end pipe is given by:
f1 = v / (2L)
Where:
f1 is the fundamental frequency,
v is the speed of sound (343 m/s in this case),
L is the length of the organ pipe (20 cm = 0.2 m).
Plugging in the values, we get:
f1 = 343 / (2 * 0.2)
f1 = 1715 Hz
The second frequency (first harmonic) for a closed-end pipe is twice the frequency of the fundamental frequency:
f2 = 2 * f1
f2 = 2 * 1715
f2 = 3430 Hz
The third frequency (second harmonic) is three times the fundamental frequency:
f3 = 3 * f1
f3 = 3 * 1715
f3 = 5145 Hz
(B) When both ends of the organ pipe are open:
The first frequency (fundamental frequency) for an open-end pipe is given by:
f1 = v / (2L)
Since both ends are open, the length of the pipe is equal to half of a wavelength. Therefore, the fundamental frequency is the same as the first harmonic for a closed-end pipe:
f1 = 1715 Hz (same as in case A)
The second frequency (second harmonic) for an open-end pipe is twice the frequency of the fundamental frequency:
f2 = 2 * f1
f2 = 2 * 1715
f2 = 3430 Hz (same as in case A)
The third frequency (third harmonic) is three times the fundamental frequency:
f3 = 3 * f1
f3 = 3 * 1715
f3 = 5145 Hz (same as in case A)
In summary:
For an organ pipe with only one end open:
- First frequency: 1715 Hz
- Second frequency: 3430 Hz
- Third frequency: 5145 Hz
For an organ pipe with both ends open:
- First frequency: 1715 Hz
- Second frequency: 3430 Hz
- Third frequency: 5145 Hz