The lowest frequency in the audible range is 20Hz.
A)What is the length of the shortest open-open tube needed to produce this frequency?
B)What is the length of the shortest open-closed tube needed to produce this frequency?
To determine the length of the shortest open-open tube needed to produce a frequency of 20Hz, you can use the formula:
L = (v / 2f)
Where:
L is the length of the tube,
v is the velocity of sound, and
f is the frequency.
Since the question doesn't provide the velocity of sound, we can use the standard value of approximately 343 meters per second for dry air at room temperature.
A) Length of the shortest open-open tube:
L = (343 / (2 * 20))
= 8.575 meters
Therefore, the length of the shortest open-open tube needed to produce a frequency of 20Hz is approximately 8.575 meters.
For the length of the shortest open-closed tube, we need to adjust the formula, as the open end of the tube will become closed.
B) Length of the shortest open-closed tube:
L = (v / 4f)
L = (343 / (4 * 20))
= 4.2875 meters
Therefore, the length of the shortest open-closed tube needed to produce a frequency of 20Hz is approximately 4.2875 meters.
To find the length of the shortest open-open tube needed to produce a frequency of 20Hz, we can use the formula:
λ = 2L
Where:
λ is the wavelength of the sound wave, and
L is the length of the tube.
First, we need to find the wavelength of a sound wave with a frequency of 20Hz. The speed of sound in air is generally around 343 meters per second.
Using the formula:
v = λ * f
Where:
v is the speed of sound, and
f is the frequency of the sound wave.
We can rearrange the formula to solve for wavelength (λ):
λ = v / f
Plugging in the values:
λ = 343 m/s / 20 Hz
λ = 17.15 meters
Now, since an open-open tube has both ends open, half of the wavelength of the sound wave (λ/2) is equal to the length of the tube (L):
L = λ/2
L = 17.15 m / 2
L = 8.575 meters
Therefore, the length of the shortest open-open tube needed to produce a frequency of 20Hz is approximately 8.575 meters.
Moving on to the length of the shortest open-closed tube needed to produce a frequency of 20Hz, we use the same formula:
λ = 4L
Since this tube has one closed end, the length of the tube (L) is equal to one-fourth of the wavelength of the sound wave (λ/4):
L = λ/4
L = 17.15 m / 4
L = 4.29 meters
Therefore, the length of the shortest open-closed tube needed to produce a frequency of 20Hz is approximately 4.29 meters.
A) L=λ/2=v/2f
B) L=λ/4=v/4f
v is the speed of sound