Answer:
2.625 m
Explanation:
To find the length of the pipe, we can use the formula for the fundamental frequency of a pipe that is open at both ends. The fundamental frequency (first harmonic) for such a pipe is given by the equation:
[tex]f_1 = \dfrac{v}{2L}[/tex]
Where:
Plug in our given values and solve for 'L':
[tex]\Longrightarrow 420 \text{ Hz} = \dfrac{320 \text{ m/s}}{2L}\\\\\\\\\Longrightarrow L =420 \text{ Hz} \times \dfrac{2}{320 \text{ m/s}}\\\\\\\\\therefore L = \boxed{2.625 \text{ m}}[/tex]
Thus, the pipe is 2.625 meters long.
To find the length of an open pipe with a fundamental frequency of 420 Hz and a speed of sound of 320 m/s, you can rearrange the fundamental frequency formula for open pipes and calculate the length to be approximately 38.1 cm.
To determine the length of the pipe that is open at both ends with a fundamental frequency of 420 Hz, we can use the formula for the fundamental frequency of a tube open at both ends, which is:
f = v / (2L)
Where:
We can rearrange this formula to solve for L:
L = v / (2f)
Plugging in the given values:
L = 320 m/s / (2 × 420 Hz)
L = 320 m/s / 840 H
L = 0.38095 meters, or approximately 38.1 cm
Therefore, the length of the pipe that resonates at a fundamental frequency of 420 Hz when the speed of sound is 320 m/s is about 38.1 cm.
