#harmonic

Doppler Effect

A pipe open at both ends has a length of 0.34 m and resonates with a source of frequency 1000 Hz. What is the harmonic n

**Frequency shift** proportional to source speed relative to wave speed v. Understanding sign convention for approaching versus receding is key, with approaching increasing frequency and receding decreasing, central to Doppler applications. v_n = (n v/2L) . 1000 = (n × 340/2 × 0.34) = (n × 340/0.68) . 1000 = n × 500 ⇒ n = (1000/500) = 2 . Second harmonic. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2, 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 0.425 m and resonates with a source of frequency 800 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) . 800 = (n × 340/2 × 0.425) = (n × 340/0.85) . 800 = n × 400 ⇒ n = (800/400) = 2 . Second harmonic. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2, 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 0.8 m and resonates with a source of frequency 637.5 Hz. What is the harmonic n

**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) . 637.5 = (n × 340/2 × 0.8) = (n × 340/1.6) . 637.5 = n × 212.5 ⇒ n = (637.5/212.5) = 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 0.6 m and resonates with a source of frequency 850 Hz. What is the harmonic num

**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) . 850 = (n × 340/2 × 0.6) = (n × 340/1.2) . 850 = n × 283.33 ⇒ n ≈ (850/283.33) ≈ 3 . Third harmonic (exact: v₃ = 3 × 340 / 1.2 = 850 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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