Practice question
Question
A string of length 1.5 m fixed at both ends has a wave speed of 45 m/s. What is the frequency of its
fifth harmonic?
Explanation
**Interference of waves** produces enhancement or cancellation based on phase. Two equal amplitude waves out of phase by π cancel completely, A = 0, while in-phase superposition doubles amplitude to 2a, demonstrating energy redistribution without violation of conservation. v_n = (n v/2L) . Fifth harmonic ( n = 5 ): v₅ = (5 × 45/2 × 1.5) = (225/3) = 75 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 75 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.
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