Question
The length of a closed pipe is 160 mm calculate the wavelength and the frequency of first overtone and third harmonic
Answers
GPT 3.5
To calculate the wavelength and frequency of the first overtone and third harmonic in a closed pipe, we can use the formula:
c = 2Lf
Where:
c = speed of sound (approximately 343 m/s)
L = length of the pipe (converted to meters)
f = frequency
First, let's convert the length of the pipe from mm to meters:
L = 160 mm = 160/1000 m = 0.16 m
1) First overtone (second harmonic):
In the first overtone, we have one additional antinode compared to the fundamental mode. This means that the length of the pipe is half the wavelength.
Wavelength (λ) = 2L = 2 * 0.16 m = 0.32 m
To calculate the frequency, we rearrange the formula:
f = c / 2L = 343 m/s / (2 * 0.16 m) ≈ 1067.19 Hz
Therefore, the wavelength of the first overtone is 0.32 m and the frequency is approximately 1067.19 Hz.
2) Third harmonic:
In the third harmonic, there are two additional antinodes compared to the fundamental mode. This means that the length of the pipe is one-third of the wavelength.
Wavelength (λ) = 3L = 3 * 0.16 m = 0.48 m
To calculate the frequency:
f = c / λ = 343 m/s / 0.48 m ≈ 714.58 Hz
Therefore, the wavelength of the third harmonic is 0.48 m and the frequency is approximately 714.58 Hz.
c = 2Lf
Where:
c = speed of sound (approximately 343 m/s)
L = length of the pipe (converted to meters)
f = frequency
First, let's convert the length of the pipe from mm to meters:
L = 160 mm = 160/1000 m = 0.16 m
1) First overtone (second harmonic):
In the first overtone, we have one additional antinode compared to the fundamental mode. This means that the length of the pipe is half the wavelength.
Wavelength (λ) = 2L = 2 * 0.16 m = 0.32 m
To calculate the frequency, we rearrange the formula:
f = c / 2L = 343 m/s / (2 * 0.16 m) ≈ 1067.19 Hz
Therefore, the wavelength of the first overtone is 0.32 m and the frequency is approximately 1067.19 Hz.
2) Third harmonic:
In the third harmonic, there are two additional antinodes compared to the fundamental mode. This means that the length of the pipe is one-third of the wavelength.
Wavelength (λ) = 3L = 3 * 0.16 m = 0.48 m
To calculate the frequency:
f = c / λ = 343 m/s / 0.48 m ≈ 714.58 Hz
Therefore, the wavelength of the third harmonic is 0.48 m and the frequency is approximately 714.58 Hz.