A resonating glass tube closed at one end is 4.0 cm wide and 47.0 cm long. What are the frequencies of the first two harmonics for the resonating tube? The speed of sound in air at this temperature is 346 m/s.

a. 736 Hz, 221 Hz

c. 184 Hz, 552 Hz

b. 651 Hz, 195 Hz

d. 184 Hz, 368 Hz

For the tube of length L the fundamental or first harmonic occurs when the wavelength of the sound is four times the length of the tube or: λ₁=4*L. So the fundamental wavelength λ₁ is:

λ₁=4*0.47=1.88 m.

To get the frequency of the sound we need the formula: v=λ*f where v is the speed of sound, λ is the wavelength and f is the frequency of sound.

So fundamental frequency f₁=v/λ₁ = 346/1.88 = 184 Hz.

To get some other or nth harmonic we need to multiply the fundamental frequency f₁ by the number n. The formula for nth harmonic is: fn=n*f₁. n is the number of the harmonic we are looking for. So in our case, n=2.

f₂=2*f₁=2*184 Hz=368 Hz.

So the frequency of the first and second harmonic is: f₁=184 Hz and f₂=368 Hz.