A length of organ pipe is closed at one end.
If the speed of sound is 344 m/s, what length of pipe is needed to obtain a fundamental frequency of 74 Hz?
Answer in units of m.
The closed end provides a reflection that is 180 degrees phase shift, so the path up, and the path back must provide 180 degrees total, or the pipe is lambda/4 in length.
To find the length of the pipe needed to obtain a fundamental frequency of 74 Hz, we can use the formula for the speed of sound in a closed pipe:
v = (2L * f) / n
Where:
v is the speed of sound (344 m/s),
L is the length of the pipe,
f is the fundamental frequency (74 Hz),
and n is the harmonic number (1 for the fundamental frequency).
Rearranging the formula, we can solve for L:
L = (v * n) / (2 * f)
Substituting the given values:
L = (344 m/s * 1) / (2 * 74 Hz)
L = 344 m/s / 148 Hz
L ≈ 2.32 m
Therefore, a length of approximately 2.32 meters is needed to obtain a fundamental frequency of 74 Hz.
To find the length of the organ pipe needed to obtain a fundamental frequency of 74 Hz, we can use the speed of sound equation for a closed organ pipe, given by:
v = (2L / λ) f
Where:
- v is the speed of sound (344 m/s)
- L is the length of the pipe
- λ is the wavelength of the fundamental frequency
- f is the fundamental frequency
First, we need to find the wavelength of the fundamental frequency. The wavelength (λ) is given by the equation:
λ = v / f
Substituting the given values, we have:
λ = 344 m/s / 74 Hz
λ ≈ 4.649 m
Now, we can substitute the value of λ into the speed of sound equation and solve for L:
344 m/s = (2L / 4.649 m) × 74 Hz
To isolate L, we can rearrange the equation:
L = (λ / 2) × (v / f)
L = (4.649 m / 2) × (344 m/s / 74 Hz)
L ≈ 1.546 m
Therefore, the length of the organ pipe needed to obtain a fundamental frequency of 74 Hz is approximately 1.546 meters.