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 funda- mental frequency of 70 Hz? Answer in units of m.
To find the length of the organ pipe needed to obtain a fundamental frequency of 70 Hz, we can use the formula for the speed of sound in a closed-end pipe:
v = (2(L / λ)) * f
Where:
v = speed of sound (344 m/s)
L = length of the pipe
λ = wavelength of the sound wave
f = frequency of the sound wave (fundamental frequency)
Since we are looking for the length of the pipe, we can rearrange the formula to solve for L:
L = (v / (2 * f)) * λ
Since the pipe is closed at one end, the wavelength of the sound wave can be determined using the formula:
λ = 4L
Substituting this into the previous equation, we get:
L = (v / (2 * f)) * 4L
Simplifying the equation, we have:
1 = (v / (2 * f)) * 4
Now, we can solve for L:
L = (v / (2 * f)) * 4
L = (344 / (2 * 70)) * 4
L = 4.914
Therefore, a length of approximately 4.914 meters is needed to obtain a fundamental frequency of 70 Hz in a closed-end organ pipe.
To find the length of the pipe needed to obtain a fundamental frequency of 70 Hz, we can use the formula for the speed of sound in a tube closed at one end:
v = (2Lf) / n
Where:
- v is the speed of sound
- L is the length of the pipe
- f is the frequency
- n is the harmonic number (in this case, it is 1 for the fundamental frequency)
Since we are given the speed of sound (v = 344 m/s) and the frequency of the fundamental mode (f = 70 Hz), we can rearrange the formula to solve for the length of the pipe:
L = (v * n) / (2f)
Substituting the given values:
L = (344 m/s * 1) / (2 * 70 Hz)
L = 172 / 140
L ≈ 1.2286 m
Therefore, a length of approximately 1.2286 meters is needed to obtain a fundamental frequency of 70 Hz.