Question

A bugle can be thought of as an open-end pipe. If a bugle were straightened out, it would be 2.65 m long. a. If the speed of sound is 343 m/s, find the lowest frequency (i.e., the largest wavelength) that can resonate in a bugle. (64.72 Hz) b. Find the next two higher resonant frequencies in the bugle. What harmonics are they

Answer 1

Answer

given,

Length of pipe, L = 2.65 m

speed of sound, v = 343 m/s

Pipe is open end Pipe

a) Lowest frequency

  condition, for open end pipe

     $\lambda_1 = 2 L$

     $\lambda_1 = 2\times 2.65$  

     $\lambda_1= 5.30 m$

   For lowest frequency

    $f_1 = n\dfrac{v}{\lambda_1}$

     n = 1

    $f_1 = \dfrac{343}{5.30}$

           f₁ = 64.72 Hz

b) For second frequency in bugle

        n = 2

   $f_2 =2\times \dfrac{343}{5.30}$

          f₂ = 129.43 Hz

   for n = 3

   $f_3 =3\times \dfrac{343}{5.30}$

          f₃ = 194.16 Hz