Question

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?

Answer 1

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

Step-by-step explanation:

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

v =
`v_o \ \sqrt{1+ (T)/(273) }`

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

v = 331
`\sqrt{1 + (24.5)/(273) }`

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