A student is blowing against the mouthpiece of a 668mm flute (open at both ends) causing it to resonate. (The air inside and outside the flute is 24.5°C) 1) what is the speed of the sound in the flute?

2) what is the fundamental frequency of the note produced?

3) what is the wavelength of the sound wave?

a)     v = 345.5 m / s,  b)    f = 183.8 Hz,  c)  λ = 1,336 m

Explanation:

a) the speed of sound depends on the density of the medium and this depends on the temperature, therefore

         v =

where v₀ is the speed of sound at 0ºC v₀ = 331 m / s

         v = 331  

         v = 345.5 m / s

c) In the exercise they indicate that the flute is a tube with the two ends open, so that at each end there is a belly, the resonance is

        λ / 2 = L

        λ = 2L

        λ = 2 0.668

        λ = 1,336 m

b) let's apply the relationship between speed, wavelength and frequency

        v = λ f

        f = v /λ

        f = 345.5 / 1.336

        f = 183.8 Hz