Question

La columna de aire en el interior de un clarinete fibra de tal manera que se forma ondas estacionarias con un nodo en un extremo y un vientre en el otro. Esta propiedad le da su caracterisca sonoridad. Si el instrumento tiene 50 cm de largo, ¿cual es la longitud de onda de su sonodo mas bajo que produce?

Answer 1

200 cm

Step-by-step explanation:

To find the wavelength of the least sound produced by the air column, you take into account that for the first mode you have that the wavelength is four times the length of the column:

`\lambda=4L`

This is because the sound is reflected in the column in such a way that only one quarter of the wavelength of the sound, allows one to obtain a mode of resonance into the air column.

Furthermore, this correspond to the least frequency because in this system the frequency is given by:

`f_n=(nv_s)/(4L)=(v_s)/(\lambda_n)\\\\\lambda=4L`

It is clear that for n=1 you obtain the least frequency.

By replacing the value of L you obtain:

`\lambda=4(50cm)=200cm`

hence, the wavelength is 200 cm