In this experiment our goal is to measure the speed of sound in air. We will be doing this by using hollow tubes and measuring the sound that comes out of them. The hollow tube will be spun around fast enough until it produces a noise. We will record two different noises at different octaves with the tube and record both
sounds. After analyzing the sound vs. time and approximating it with logger pro we determined that the angular frequency of the two different sounds were
ω_1 = 3859 rad/s + 0.4736 rad/s, ω_2 = 5068 rad/s + 1.106 rad/s.
Using this formula ω = 2πf, where f is the frequency, we can rearrange this equation into f = ω/2π and we can determine that f_1 = 614 Hz + 0.753 Hz and f_2 = 806 Hz + 0.176Hz.
We can also determine the wavelength by using the formula v = fλ. In this equation v is the speed of sound and λ is the wave length. When we rearrange this equation we have v/f = λ. λ_1 = 0.554 m + 0.005m and λ_2 = 0.422m + 0.005m.
We also know that λ_1/2 * (2n+1) = L and λ_2/2 * (2n+3) = L, n is the number of harmonics and L is the total length of the wave. To find n we can rearrange the two equations together and it results in λ_1/λ_2 = (2n+3)/(2n+1).
We began by finding the angular frequency with loggerpro and find the frequency from that information. Once inputting our values we can determine that n is 2.694 which we can round up to 3.
To determine the length of L we can use λ*n/2 = L
L = 0.831m + 0.015m
We could not measure the actual length of the pipe so percent error cannot be calculated. The error was determined by adding up the associated errors.
ω_1 = 3859 rad/s + 0.4736 rad/s, ω_2 = 5068 rad/s + 1.106 rad/s.
Using this formula ω = 2πf, where f is the frequency, we can rearrange this equation into f = ω/2π and we can determine that f_1 = 614 Hz + 0.753 Hz and f_2 = 806 Hz + 0.176Hz.
We can also determine the wavelength by using the formula v = fλ. In this equation v is the speed of sound and λ is the wave length. When we rearrange this equation we have v/f = λ. λ_1 = 0.554 m + 0.005m and λ_2 = 0.422m + 0.005m.
We also know that λ_1/2 * (2n+1) = L and λ_2/2 * (2n+3) = L, n is the number of harmonics and L is the total length of the wave. To find n we can rearrange the two equations together and it results in λ_1/λ_2 = (2n+3)/(2n+1).
Conclusion
We began by finding the angular frequency with loggerpro and find the frequency from that information. Once inputting our values we can determine that n is 2.694 which we can round up to 3.
To determine the length of L we can use λ*n/2 = L
L = 0.831m + 0.015m
We could not measure the actual length of the pipe so percent error cannot be calculated. The error was determined by adding up the associated errors.
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