Suppose you used a 300 Hz tuning fork to produce resonant frequency in a tube whose diameter is 3.0 cm. At what length of the tube will you the resonant frequency if the air temperature inside the tube is 25 C. Assume that the tube is closed at one end.

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To find the length of the tube at which the resonant frequency occurs, we can use the formula for the resonant frequency of a closed-ended tube:

f = (2n - 1)*(v/4L)

Where:
f = resonant frequency
n = harmonic number (1, 2, 3, ...)
v = speed of sound in air
L = length of the tube

First, we need to calculate the speed of sound in air at the given temperature. The speed of sound in air is given by the equation:

v = 331.4 + 0.6*T

Where:
v = speed of sound in air (in m/s)
T = temperature in Celsius

Plugging in the temperature T = 25°C, we can calculate the speed of sound in air:

v = 331.4 + 0.6*25
v = 346.4 m/s

Next, we need to rearrange the formula for the resonant frequency to solve for the length of the tube:

L = (2n - 1)*(v/4f)

We know the frequency of the tuning fork is 300 Hz, so let's plug that into the formula:

L = (2n - 1)*(346.4/4*300)

Now, let's calculate the length using different harmonic numbers (n = 1, 2, 3, ...), until we find the length at which the resonant frequency occurs:

For n = 1:
L = (2*1 - 1)*(346.4/4*300) = 0.5776 m or 57.76 cm

For n = 2:
L = (2*2 - 1)*(346.4/4*300) = 1.1552 m or 115.52 cm

For n = 3:
L = (2*3 - 1)*(346.4/4*300) = 1.7328 m or 173.28 cm

...

Continue calculating the length for higher values of n until you find the length at which the resonant frequency occurs.

Note: Since the tube is closed at one end, the resonant frequencies occur at odd harmonic numbers (n = 1, 3, 5, ...).