Yes, you do need the speed of sound. The wavelength in air is NOT the wavelength in the string. What is true is that the frequency in air is the same as the frequency in string.
First of all, I do not think that the speed of the sound in air matters, and I just used the formula Length= n*(wave length)/2, so L=3(3.47)/2 = about 5m. Now this is very unrealistic. So what do you think??If a third harmonic is generated on a guitar string, so that the sound produced in air has a wavelength of 3.47m, what is the length of the string? Assume the speed of waves on the guitar's string is 500 m/s and in air is 334m/s.
Thank you for your time.