#sound speed

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 0.4 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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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

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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

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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.

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 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

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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.

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 0.5 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

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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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.28 m and a speed of sound of 336 m/s. What is the frequency of its fourth har

**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 = 3 for fourth harmonic. v₃ = (3 + (1/2)) (336/2 × 0.28) = 3.5 × (336/0.56) = 3.5 × 600 = 2100 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2100 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 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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