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#speed of sound

21 public questions tagged with this topic.

Sound Waves, Reflection and Characteristics

A steel rod of length 2 m has a fundamental frequency of longitudinal vibrations of 1.25 kHz. What is the speed of sound

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 1250 = (v/2 × 2) ⇒ v = 1250 × 4 = 5000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 5000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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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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Sound Waves, Reflection and Characteristics

A steel rod of length 1.5 m has a fundamental frequency of longitudinal vibrations of 2 kHz. What is the speed of sound

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 2000 = (v/2 × 1.5) ⇒ v = 2000 × 3 = 6000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 6000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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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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Sound Waves, Reflection and Characteristics

The speed of sound in air at STP is calculated using Newton’s formula as 280 m/s. If the actual speed is 331 m/s, what i

**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. Newton’s formula: v = √((P/rho)) = 280 m/s . Laplace correction: v = √((gamma P/rho)) = 331 m/s . Divide: (331/280) = √(gamma) . √(gamma) = 1.182 , so gamma = (1.182)² ≈ 1.4 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1.4, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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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

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Sound Waves, Reflection and Characteristics

Why does the speed of sound increase with temperature in a gas?

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. Speed of sound in a gas is v = √((gamma P/rho)) , and since P/rho ∝ T (ideal gas law), higher temperature increases molecular velocity, thus increasing v . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Molecular velocity increases, 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 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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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

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Vibrations of Air Columns - Open and Closed Pipes

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

**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 closed pipe: 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.

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

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Wave Speed, Energy and Power

Why is the speed of sound higher in solids than in liquids?

**Energy transport** in waves scales with amplitude squared A² and frequency squared ω². Wave speed determines propagation rate, and understanding T and μ allows quantitative prediction of v and associated frequencies. Solids have greater elastic moduli (bulk and shear) than liquids, increasing the speed of sound ( v = √((elastic modulus/rho)) ), despite higher density, as elasticity dominates. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Greater elastic modulus, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Speed, Energy and Power

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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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