What is the fundamental frequency, the first three overtones of an organ pipe that is 100cm in length ans is closed on one end and open on the other? Take the speed of sound to be 345 m/s.
The pipe is 1/4 lambda long
lambda=4m, so f=345/4 hz That is the fundamental.
Thank you very much!
To find the fundamental frequency and the first three overtones of a closed-open organ pipe, we can use the formula:
fn = (n * v) / (4 * L)
where:
- fn is the frequency of the nth overtone,
- v is the speed of sound,
- n is the overtone number,
- L is the length of the pipe.
Given:
- Length of the pipe (L): 100 cm = 1 m (converted to meters)
- Speed of sound (v): 345 m/s
Let's calculate the frequencies step-by-step:
Step 1: Calculate the fundamental frequency (n=1)
f1 = (1 * v) / (4 * L)
f1 = (1 * 345) / (4 * 1)
f1 = 345 / 4
f1 = 86.25 Hz
Step 2: Calculate the first overtone (n=2)
f2 = (2 * v) / (4 * L)
f2 = (2 * 345) / (4 * 1)
f2 = 690 / 4
f2 = 172.5 Hz
Step 3: Calculate the second overtone (n=3)
f3 = (3 * v) / (4 * L)
f3 = (3 * 345) / (4 * 1)
f3 = 1035 / 4
f3 = 258.75 Hz
Therefore, the fundamental frequency is 86.25 Hz, the first overtone is 172.5 Hz, and the second overtone is 258.75 Hz.
To determine the fundamental frequency and the first three overtones of an organ pipe that is 100 cm in length and is closed on one end and open on the other, we can use the formula for the frequency of a closed-closed organ pipe as follows:
f = (nv)/(2L)
Where:
f is the frequency
n is the harmonic number (1 for the fundamental frequency, 2 for the first overtone, 3 for the second overtone, and so on)
v is the speed of sound
L is the length of the organ pipe
Given that the length of the organ pipe is 100 cm (which is equivalent to 1 meter) and the speed of sound is 345 m/s, we can substitute these values into the formula to find the frequencies.
For the fundamental frequency (n = 1):
f₁ = (1 * 345)/(2 * 1)
f₁ = 172.5 Hz
For the first overtone (n = 2):
f₂ = (2 * 345)/(2 * 1)
f₂ = 345 Hz
For the second overtone (n = 3):
f₃ = (3 * 345)/(2 * 1)
f₃ = 517.5 Hz
Therefore, the fundamental frequency of the organ pipe is 172.5 Hz, the first overtone is 345 Hz, and the second overtone is 517.5 Hz.