6) Consider a 2.500 m-long tube that is open on both ends in a laboratory on a day when the speed of sound is 345m/s

a) Sketch the fundamental, or first harmonic, for this tube.

b) How many wavelengths constitute the fundamental?

c) Calculate the frequency of the fundamental.

d) Calculate the frequency of the third harmonic.

a) Please find attached the diagram of the fundamental or first harmonics of tube the created with Microsoft Word

b) The fundamental frequency consists of half wavelength

c) The frequency of the fundamental is 69 Hz

d) The frequency of the third harmonic is 207 Hz

Explanation:

The given parameters of the tube are;

The length of the tube, L = 2.5 m

The speed of sound, c = 345 m/s

a) Please find the diagram of the first harmonics created with Microsoft Word

b) The wavelength of the fundamental frequency, λ₁ = 2·L

Therefore, λ₁ = 2 × 2.5 m = 5.0 m

Therefore, the fundamental frequency consists of 1/2 wavelength

c) The frequency = (The speed of the wave)/(The wavelength of the wave)

The frequency of the fundamental frequency, f₁ = 345 m/s/(5.0 m) = 69 Hz

f₁ = 69 Hz

d) The frequency of the third harmonic, f₃ = 3 × f₁  

∴ f₃ = 3 × 69 Hz = 207 Hz

The frequency of the third harmonic, f₃ = 207 Hz

c. magnitude and direction