The clarinet is well modeled as a cylindrical pipe that is open at one end and closed at the other. Find the wavelength and frequency of the third normal mode of vibration of a clarinet's air column with effective length of 0.401 m. Take 342 m/s for the speed of sound inside the instrument.

The characteristics of standing waves in tubes allows to find the results for the third harmonic of the clarinet are:

Standing waves are formed when a wave collides with an obstacle and is reflected, the sum of the incident wave and the reflected wave forms a standing wave that does not move in time. There are several types of obstacles:

They indicate that the clarinet is approximated to a tube with one end open and the other closed, therefore at the closed end we have a node and at the open end a antinode, in the adjoint we see a diagram of the resonance, the expression for the resonance should be:

      L =                1st harmonic

       L =             3th harmonic

      L =    General term

where L is the length of the tube, λ the wavelength and n an integer.

Ask for the wavelength of the third harmonic m = 3

     λ =

     λ  =  

     λ  = 0.5365 m

The speed of the wave is related to the product of the wavelength and the frequency.

     v = λ f

     f =  

Let's calculate.

     f =  

     f = 639.7 Hz

In conclusion, using the characteristics of standing waves in tubes we can find the results for the third harmonic of the clarinet are:

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wavelength is = 0.05m

frequency is = 639.65 Hz

Explanation:

F= 3V/4L

(3 x 342)/(4 x 0.401) = 639.65Hz

Wavelenght =4L/3

wavelength =(4x0.401)/3 = 0.05m

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