Question

A bugle can be represented by a cylindrical pipe of length L=1.35m. The pipe is open at one end and closed at the other end(the end with the mouthpiece). Calculate the longest three wavelengths of standing waves inside the bugle. Also calculate the three most frequencies and the three longest wavelengths of the sound that is produced in the air around the bugle.

Answer 1

For one end open pipe we have condition as below,

L= nλ_n/4      …where n=1,3,5,……

λ_n = 4L/n

f_n = v/λ_n = nv/4L

For n=1,

λ₁ = 4L/1 = 4L = 4*1.35 = 5.4 m

f₁ = v/λ₁ = (343m/s)/(5.4m) = 63.52 Hz

For n=3,

λ₃ = 4L/3 = 4L/3 = 4/3*1.35 = 1.8 m

f₃ = v/λ₃ = (343m/s)/(1.8m) = 190.56 Hz

For n=5,

λ ₅ = 4L/5 = 4L/5 = 4/5*1.35 = 1.08 m

F₅ = v/λ₅ = (343m/s)/(1.08m) = 317.56 Hz