An organ pipe is open at both ends. It is producing sound at its sixth harmonic, the frequency of which is 257 Hz. The speed of sound is 343 m/s. What is the length of the pipe?

m

open: doesn't this mean the length is equal to n/2 wavelengths, where n= odd?

Yes, you are correct. For an open organ pipe, the length of the pipe is equal to an odd integer multiple of half the wavelength of the sound produced. The formula to calculate the wavelength is given by:

λ = v / f

where λ is the wavelength, v is the speed of sound, and f is the frequency.

In this case, the frequency is 257 Hz and the speed of sound is 343 m/s. Plugging these values into the formula:

λ = 343 / 257

Now, we need to find the length of the pipe. Since the pipe is open at both ends, the length will be an odd multiple of half the wavelength:

L = (2n - 1) * (λ / 2)

where L is the length of the pipe, and n is an integer.

To find the length, we need to determine the value of n.

Since the frequency is the sixth harmonic, it means the sound produced is at six times the fundamental frequency. Therefore, n = 6.

Plugging in the values:

L = (2*6 - 1) * (λ / 2)
L = 11 * (λ / 2)

Now, we can calculate the length of the pipe by substituting the value of λ we obtained earlier:

L = 11 * (343 / 257)

Calculating this expression will give you the length of the pipe in meters.