Question

Zoe is striking a tuning fork that is held near the mouth of a narrow plastic pipe that is partially underwater. The plastic pipe is raised and the first sound is heard when the air column is 9.0 cm long. The temperature in the room is 20ºC. Calculate the length of the sir column for the 2nd and 3rd resonances. a) 27.5 cm and 56 cm Ob) 0.18 and 0.30 m c) 13.5 m and 22.5 cm d) 0.27 m and 0.45 m

Answer 1

Let's list some variables:

v: speed of sound in air at 20ºC; v = 343 m/s

Since the first sound is heard when the air column is 9cm long, the wavelength of the wave is 4 times that, so 36cm. (λ1 = 4*L = 4*9)

λ: wavelength of sound; λ = 36cm

L: length of air column

We can use the following equations for the lengths of the air column for the second and third resonances, respectively:

λ = 4L/3

λ = 4L/5

Now let's plug in the value for the wavelength of sound, λ.

36 = 4L/3

L = 27cm (second resonance)

36 = 4L/5

L = 45cm (third resonance)

Answer: 0.27m and 0.45m