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#closed pipe

22 public questions tagged with this topic.

Sound Waves, Reflection and Characteristics

A pipe closed at one end has a length of 0.25 m. What is the frequency of its third harmonic if the speed of sound is 34

**Reflection at boundaries** follows phase change rules: rigid boundary (fixed end) introduces π phase shift, inverting displacement y → -y, while free boundary reflects without phase change. Reflected wave derived by reversing propagation direction kx → -kx and applying phase shift, preserving k = 2π/λ and ω = 2πf. For closed pipe: v_n = (n + (1/2)) (v/2L) , n = 0, 1, 2, ldots . Third harmonic: n = 2 . v₂ = (2 + (1/2)) (340/2 × 0.25) = 2.5 × (340/0.5) = 1700 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields

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Sound Waves, Reflection and Characteristics

A pipe closed at one end has a length of 0.85 m and resonates at its second harmonic with a speed of sound of 340 m/s. W

**Reflection at boundaries** follows phase change rules: rigid boundary (fixed end) introduces π phase shift, inverting displacement y → -y, while free boundary reflects without phase change. Reflected wave derived by reversing propagation direction kx → -kx and applying phase shift, preserving k = 2π/λ and ω = 2πf. For closed pipe: v_n = (n + (1/2)) (v/2L) , n = 1 for second harmonic. v₁ = (1 + (1/2)) (340/2 × 0.85) = 1.5 × (340/1.7) = 300 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 300 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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Sound Waves, Reflection and Characteristics

A pipe closed at one end has a length of 0.6 m and resonates at its second harmonic with a speed of sound of 360 m/s. Wh

**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 closed pipe: v_n = (n + (1/2)) (v/2L) , n = 1 for second harmonic. v₁ = (1 + (1/2)) (360/2 × 0.6) = 1.5 × (360/1.2) = 1.5 × 300 = 450 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 450 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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Sound Waves, Reflection and Characteristics

A pipe closed at one end has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fundamental

**Reflection at boundaries** follows phase change rules: rigid boundary (fixed end) introduces π phase shift, inverting displacement y → -y, while free boundary reflects without phase change. Reflected wave derived by reversing propagation direction kx → -kx and applying phase shift, preserving k = 2π/λ and ω = 2πf. Fundamental: v₁ = (v/4L) . v₁ = (320/4 × 0.4) = (320/1.6) = 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.

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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.35 m and resonates at its fundamental frequency with a speed of sound of 350

**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. Fundamental: v₁ = (v/4L) . v₁ = (350/4 × 0.35) = (350/1.4) = 250 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 250 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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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.

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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.5 m and a speed of sound of 340 m/s. What is the frequency of its fundamental

**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. Fundamental: v₁ = (v/4L) . v₁ = (340/4 × 0.5) = (340/2) = 170 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 170 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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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.25 m and resonates at its fundamental frequency with a speed of sound of 340

**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. Fundamental: v₁ = (v/4L) . v₁ = (340/4 × 0.25) = (340/1) = 340 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 340 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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Vibrations of Air Columns - Open and Closed Pipes

In a pipe closed at one end, which harmonics are absent compared to a pipe open at both ends?

**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. A pipe closed at one end has frequencies v_n = (2n - 1) (v/4L) , producing only odd harmonics (1, 3, 5, ..). A pipe open at both ends has all harmonics (1, 2, 3, ..), so even harmonics are absent in the closed pipe. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as

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 closed at one end has a length of 0.32 m and resonates at its fundamental frequency with a speed of sound of 320

**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. Fundamental: v₁ = (v/4L) . v₁ = (320/4 × 0.32) = (320/1.28) = 250 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 250 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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Stationary Waves and Standing Waves in Strings

Why does a standing wave in a pipe closed at one end produce only odd harmonics?

**Standing wave in fixed string** has nodes at ends, quantizing modes. Fundamental n=1 has λ₁ = 2L, higher harmonics multiples of fundamental f₁. Third harmonic n=3 has three half-wavelengths in length L, f₃ = 3v/(2L), illustrating standing wave condition and boundary enforcement. The boundary condition (node at the closed end, antinode at the open end) requires the wavelength to fit L = (2n - 1) (λ/4) , allowing only odd multiples of the fundamental. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Boundary conditions, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.8 m and resonates at its third harmonic with a speed of sound of 360 m/s. Wha

**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. For closed pipe: v_n = (n + (1/2)) (v/2L) , n = 2 for third harmonic. v₂ = (2 + (1/2)) (360/2 × 0.8) = 2.5 × (360/1.6) = 2.5 × 225 = 562.5 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 562.5 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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