# Find the Second Resonant length of an air column

## Homework Statement

Find the second resonant length of an air column that resonates with a sound of frequency 1.0 kHz at 15.0 degrees Celsius under each of the following conditions.

a) the air column is closed at both ends

b) the air column is open at both ends

## Homework Equations

$$V_{s}$$ = 332 m/s + T(0.59 m/s $$\circ$$C)

v = f$$\lambda$$ therefore $$\lambda$$ = $$\frac{v}{f}$$

l = $$\frac{n \lambda}{2}$$ therefore $$\frac{2l}{n}$$ = $$\lambda$$

n = 2 for the second resonant length of an air column

## The Attempt at a Solution

$$V_{s}$$ = 332 m/s + T(0.59 m/s $$\circ$$C)
332 m/s + 15(0.59 m/s)
= 340.85
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v = f$$\lambda$$ therefore $$\lambda$$ = $$\frac{v}{f}$$

$$\frac{340.85 m/s}{1000 Hz}$$
= 34.09 cm
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$$\frac{2l}{n}$$ = $$\lambda$$

$$\lambda$$ = $$\frac{2(34.09}{2}$$
= 34.09

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The second Resonant length is 34.09 cm
I don't know how to calculate the difference between an air column open at both ends
and an air column closed at both ends. My textbook doesn't explain it clearly. I'm guessing that both types of columns have different answers but as it stands I got the same calculation for both types. Is there more to the equation that I'm missing or am I doing the whole calculation wrong.

Thanks
S