If a flute is fingered so it has a length of 0.30 m, what will be the frequency of the fundamental note you hear?

If a clarinet is fingered so it has a length exactly the same as the flute in the previous question (i.e. 0.30 m) what's the frequency of the fundamental note you hear? (Assume the air is at room temperature.
I thought the formula would be f=v/L
and f=v/(2L)wrong?

The formula you mentioned, f = v/L, is indeed the formula to calculate the frequency of a wave. However, the formula you provided, f = v/(2L), applies specifically to strings, not wind instruments like flutes and clarinets.

That being said, let's address each question separately:

1. If a flute is fingered to have a length of 0.30 m, we can use the formula f = v/λ, where f is the frequency, v is the velocity of sound, and λ is the wavelength of the sound wave produced. For a flute, the wavelength of the fundamental note (the lowest frequency tone) is twice the length of the flute. Therefore, the wavelength is 2 * 0.30 m = 0.60 m. Since the speed of sound in air at room temperature is approximately 343 m/s, we can substitute these values into the formula: f = 343 m/s / 0.60 m = 571.67 Hz.

2. Similarly, if a clarinet is fingered to have a length of 0.30 m, we can use the same formula. The wavelength for the fundamental note of a clarinet is four times the length of the clarinet. Thus, the wavelength is 4 * 0.30 m = 1.20 m. Using the speed of sound in air at room temperature (343 m/s), we can substitute these values into the formula: f = 343 m/s / 1.20 m = 285.83 Hz.

To summarize, the frequency of the fundamental note in a flute with a length of 0.30 m is approximately 571.67 Hz, while the frequency of the fundamental note in a clarinet with the same length is approximately 285.83 Hz.