If sounds produced by the human vocal cords are approximated as waves on a string fixed at both ends, and the average length of a vocal cord is 15 mm, what is the fundamental frequency of the sound? (note: use 3 m/s for the speed of sound through the vocal cord.)

The fundamental frequency of the sound is: 100 Hertz

Explanation:

We need to remember that the period (T) which unit is the seconds, is the inverse of the frequency (f), which unit is the Hertz, and we call wavelength (λ) to space which the sound is traveling, which unit is the meter. So that the equation which related those variables is: λ = v x T = v / f

where v is the speed of the sound, but the wavelength of the fundamental modo for a string fixed at both ends is: λn=2*L/n; in this case n=1 (fundamental mode) so λ1=(2*0,015)/1 = 0.030 (m). Replaced the values give us for the exercise, we get: λ= 0.030 (m), v = 3 (m/s) so that f = v / λ = 3 (m/s) / 0.030 (m) so the answer is λ = 100 Hertz.

no. dot product   =0 when vecs at right angles