#open pipe

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

View Details

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

View Details

Doppler Effect

A pipe 0.5 m long, open at both ends, resonates with a 340 Hz source. What is the harmonic number if the speed of sound

**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. For open pipe: v_n = (n v/2L) . Given: v = 340 m/s , L = 0.5 m , v_n = 340 Hz . 340 = (n × 340/2 × 0.5) ⇒ 340 = 340n ⇒ n = 1 . First harmonic (fundamental mode). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

View Details

Sound Waves, Reflection and Characteristics

A pipe open at both ends has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fourth harm

**Sound wave reflection** at rigid wall behaves like string fixed end, displacement inverted. Equation of reflected wave includes sign change and direction reversal, amplitude unchanged but sign may flip, explaining standing wave formation with incident wave. For open pipe: v_n = (n v/2L) . Fourth harmonic ( n = 4 ): v₄ = (4 × 320/2 × 0.4) = (1280/0.8) = 1600 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1600 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details

Sound Waves, Reflection and Characteristics

A pipe open at both ends has a length of 0.25 m and a speed of sound of 340 m/s. What is the frequency of its second har

**Sound wave reflection** at rigid wall behaves like string fixed end, displacement inverted. Equation of reflected wave includes sign change and direction reversal, amplitude unchanged but sign may flip, explaining standing wave formation with incident wave. For open pipe: v_n = (n v/2L) . Second harmonic ( n = 2 ): v₂ = (2 × 340/2 × 0.25) = (680/0.5) = 1360 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1360 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Sound Waves, Reflection and Characteristics

View Details

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

View Details

Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends has a length of 0.85 m and a speed of sound of 340 m/s. What is the frequency of its first harm

**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. For open pipe: v_n = (n v/2L) . First harmonic ( n = 1 ): v₁ = (340/2 × 0.85) = (340/1.7) = 200 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 200 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

View Details

Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends has a length of 0.3 m and a speed of sound of 330 m/s. What is the frequency of its second harm

**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. For open pipe: v_n = (n v/2L) . Second harmonic ( n = 2 ): v₂ = (2 × 330/2 × 0.3) = (660/0.6) = 1100 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1100 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

View Details

Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends has a length of 0.51 m and a speed of sound of 340 m/s. What is the frequency of its third harm

**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 open pipe: v_n = (n v/2L) . Third harmonic ( n = 3 ): v₃ = (3 × 340/2 × 0.51) = (1020/1.02) = 1000 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1000 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

View Details

Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends resonates at 510 Hz with a speed of sound of 340 m/s. What is its length?

**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/2L) . 510 = (340/2L) ⇒ 2L = (340/510) ⇒ 2L = (2/3) ⇒ L = 0.333 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.33 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

View Details

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

View Details

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

View Details