#harmonic number

Doppler Effect

A pipe open at both ends has a length of 0.68 m and resonates with a source of frequency 750 Hz. What is the harmonic nu

**Doppler effect** describes apparent frequency shift due to relative motion between source and observer, f' = f·v/(v ∓ v_s) for source motion, f' = f·(v ± v_o)/v for observer motion, upper signs for approach increasing observed frequency. Motion towards observer compresses wavelength raising f'. v_n = (n v/2L) . 750 = (n × 340/2 × 0.68) = (n × 340/1.36) . 750 = n × 250 ⇒ n = (750/250) = 3 . Third harmonic. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends has a length of 0.45 m and resonates with a source of frequency 1133 Hz. What is the harmonic n

**Air column vibrations** depend on end conditions. Pipe closed at one end has displacement node at closed end and antinode at open, allowing only odd harmonics, fundamental f₁ = v/(4L). Open pipe has antinodes at both ends, fₙ = n·v/(2L), all harmonics present, v sound speed. v_n = (n v/2L) . 1133 = (n × 340/2 × 0.45) = (n × 340/0.9) . 1133 = n × 377.78 ⇒ n ≈ (1133/377.78) ≈ 3 . Third harmonic (exact: v₃ = 3 × 340 / 0.9 = 1133.33 Hz ). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation

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 pipe open at both ends has a length of 0.85 m and resonates with a source of frequency 600 Hz. What is the harmonic nu

**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. v_n = (n v/2L) . 600 = (n × 340/2 × 0.85) = (n × 340/1.7) . 600 = n × 200 ⇒ n = (600/200) = 3 . Third harmonic. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3, 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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Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends has a length of 0.57 m and resonates with a source of frequency 900 Hz. What is the harmonic nu

**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. v_n = (n v/2L) . 900 = (n × 342/2 × 0.57) = (n × 342/1.14) . 900 = n × 300 ⇒ n = (900/300) = 3 . Third harmonic. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3, 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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