Practice question
Question
A pipe open at both ends has a length of 0.6 m and a wave speed of 300 m/s. What is the difference in
frequency between the third and first harmonics?
Explanation
**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. v_n = (n v/2L) . First harmonic ( n = 1 ): v₁ = (300/2 × 0.6) = 250 Hz . Third harmonic ( n = 3 ): v₃ = (3 × 300/2 × 0.6) = 750 Hz . Difference: v₃ - v₁ = 750 - 250 = 500 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or
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