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#wave resonance

2 public questions tagged with this topic.

Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.5 m and resonates at its fundamental frequency with a speed of sound of 350 m

**Organ pipe modes** illustrate boundary influence. Closed pipe odd harmonic series contrasts with open pipe full series, affecting timbre. Frequency scales inversely with length, explaining pitch variation with pipe length. Fundamental: v₁ = (v/4L) . v₁ = (350/4 × 0.5) = (350/2) = 175 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 175 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries. This aligns with NCERT Class 11 treatment, emphasizing conservation, symmetry and dimensional consistency useful for CBSE, NEET and CUET.

Ref: NCERT > Physics Book > Waves > Vibrations of Air Columns - Open and Closed Pipes

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Vibrations of Air Columns - Open and Closed Pipes

A closed pipe of length 0.3 m has a speed of sound of 330 m/s. What is the frequency of its fifth harmonic?

**Resonance in pipes** occurs when length accommodates standing wave pattern. Closed pipe L = (2n-1)λ/4, so f₁ = v/(4L). Given f₁ and v, length follows L = v/(4f₁), enabling length calculation from measured resonance frequency and sound speed 330-340 m/s. For closed pipe: v_n = (n + (1/2)) (v/2L) , n = 4 for fifth harmonic. v₄ = (4 + (1/2)) (330/2 × 0.3) = 4.5 × (330/0.6) = 4.5 × 550 = 2475 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2475 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Vibrations of Air Columns - Open and Closed Pipes

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