1. 8.5 m
For an open-open tube, the frequency of the fundamental mode of vibration is given by
[tex]f=\frac{v}{2L}[/tex]
where
v is the speed of the sound wave
L is the length of the tube
In this problem, we have:
f = 20 Hz is the frequency of the fundamental mode
v = 340 m/s is the speed of sound in air
Re-arranging the equation, we find
[tex]L=\frac{v}{2f}=\frac{340 m/s}{2(20 Hz)}=8.5 m[/tex]
2. 4.25 m
For an open-closed tube instead, the frequency of the fundamental mode of vibration is given by
[tex]f=\frac{v}{4L}[/tex]
where
v is the speed of the sound wave
L is the length of the tube
In this problem, we have:
f = 20 Hz is the frequency of the fundamental mode
v = 340 m/s is the speed of sound in air
Re-arranging the equation, we find
[tex]L=\frac{v}{4f}=\frac{340 m/s}{4(20 Hz)}=4.25 m[/tex]
a. The length of the shortest open-open tube needed is 34 meters.
b. The length of the shortest open-closed tube needed is 4.25 meters.
Given the following data:
Scientific data:
Mathematically, the frequency of the fundamental mode of vibration for an open-open tube is given by this formula:
[tex]F=\frac{2V}{L}[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]20=\frac{2 \times 340}{L} \\\\L=\frac{680}{20}[/tex]
Length, L = 34 meters.
Mathematically, the frequency of the fundamental mode of vibration for an open-closed tube is given by this formula:
[tex]F=\frac{V}{4L}[/tex]
Where:
Substituting the given parameters into the formula, we have;
[tex]20=\frac{340}{4L} \\\\L=\frac{340}{80}[/tex]
Length, L = 4.25 meters.
Read more on frequency here: https://brainly.com/question/23460034
