An open organ pipe has a length of 5 cm . Identify the highest harmonic of this tube that falls within the audible range. The speed of sound in air is 340 m s ⁻¹ and the audible frequency range is 20 – 20 , 000 Hz .

Step-by-step solution

The fundamental frequency of an open organ pipe is given by f₁ = v 2L Substituting v = 340 m s ⁻¹ and L = 5 cm = 0.05 m : f₁ = 340 2 0.05 = 340 0.1 = 3400 Hz The frequencies of the harmonics for an open pipe are given by f_n = n f₁ , where n = 1, 2, 3, For the harmonic to fall within the audible range, its frequency must be less than or equal to 20 , 000 Hz : n 3400 20 , 000 n 20 , 000 3400 n 5.88 Since n must be an integer, the maximum possible value is n = 5 . Thus, the highest harmonic of this tube that falls wi