a) At T = 12°C, how long must an open organ pipe be to have a fundamental frequency of 300 Hz?

i got answer for part a that is .5642m but did not get for part b.

(b) If this pipe is instead filled with helium at 20°C, what is its fundamental frequency?
Hz

To find the answer for part b, we need to consider the effect of filling the pipe with helium instead of having it open. The speed of sound in a gas depends on the temperature and the molecular weight of the gas.

Here are the steps to find the fundamental frequency when the pipe is filled with helium:

1. Calculate the speed of sound in air at 12°C:
- The speed of sound in air can be calculated using the formula:
v = 331.5 * √(T + 273.15)
- Substituting T = 12 into the formula, we get:
v_air = 331.5 * √(12 + 273.15)
v_air ≈ 331.5 * √(285.15)
v_air ≈ 331.5 * 16.89
v_air ≈ 5585.4 m/s (rounded to one decimal place)

2. Calculate the speed of sound in helium at 20°C:
- The molecular weight of helium is 4 g/mol.
- Since helium is a lighter gas than air, the speed of sound in helium will be faster.
- We can relate the speeds of sound in two gases using the formula:
v1/v2 = √(MW2/MW1)
Where v1 and v2 are the speeds of sound in the two gases, and MW1 and MW2 are the molecular weights of the gases.
- Substituting the values, we get:
v_helium/v_air = √(MW_air/MW_helium)
v_helium/5585.4 = √(28.97 g/mol / 4 g/mol)
v_helium/5585.4 = √(7.2425)
- Solving for v_helium, we get:
v_helium ≈ 5585.4 * √(7.2425)
v_helium ≈ 5585.4 * 2.6918
v_helium ≈ 15026.2 m/s (rounded to one decimal place)

3. Calculate the wavelength of the fundamental frequency of the pipe filled with helium:
- The fundamental frequency of a pipe can be calculated using the formula:
f = v / (2L)
Where f is the frequency, v is the speed of sound in the gas, and L is the length of the pipe.
- Rearranging the formula, we get:
L = v / (2f)
- Substituting the values, we get:
L = 15026.2 / (2 * 300)
L ≈ 15026.2 / 600
L ≈ 25.04 m (rounded to two decimal places)

Therefore, the length of the pipe filled with helium at 20°C to have a fundamental frequency of 300 Hz is approximately 25.04 meters.