#longitudinal wave

What happens to the speed of a longitudinal wave in a gas if the pressure is increased while temperature remains constan

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. For an ideal gas, v = √((gamma P/rho)) , and P/rho = RT/M (constant at constant temperature). Thus, speed depends only on temperature and gamma , not pressure alone, so it remains unchanged. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Remains unchanged, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Superposition and Interference of Waves

A longitudinal wave in a medium has a speed of 1450 m/s and a density of 1100 kg/m³. What is the bulk modulus of the med

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. Speed: v = √((B/rho)) . 1450 = √((B/1100)) ⇒ 1450² = (B/1100) . B = 1450² × 1100 = 2.31 × 10⁹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2.31 × 10⁹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Wave Equation and Displacement Relation

A longitudinal wave travels in a medium with bulk modulus 1.8 × 10⁹ Pa and density 900 kg/m³. What is its speed?

**Wave equation** y(x,t) = A sin(kx - ωt + φ) describes displacement of progressive harmonic wave, where k = 2π/λ wave number (rad/m), ω = 2πf angular frequency (rad/s), v = ω/k wave speed (m/s). Sign of ωt indicates direction, amplitude A is maximum displacement. Speed: v = √((B/rho)) = √((1.8 × 10⁹/900)) = √(2 × 10⁶) ≈ 1414 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1400 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Wave Equation and Displacement Relation

A longitudinal wave in a medium has a speed of 1550 m/s and a density of 1200 kg/m³. What is the bulk modulus of the med

**Sinusoidal wave form** represents harmonic wave where each particle executes SHM. Coefficients of x and t give spatial and temporal periodicities, allowing wavelength and period extraction, basis for wave analysis in NCERT. Speed: v = √((B/rho)) . 1550 = √((B/1200)) ⇒ 1550² = (B/1200) . B = 1550² × 1200 = 2.88 × 10⁹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2.88 × 10⁹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Wave Equation and Displacement Relation

A longitudinal wave in a medium has a speed of 1700 m/s and a bulk modulus of 2.89 × 10⁹ Pa. What is the density of the

**Sinusoidal wave form** represents harmonic wave where each particle executes SHM. Coefficients of x and t give spatial and temporal periodicities, allowing wavelength and period extraction, basis for wave analysis in NCERT. Speed: v = √((B/rho)) . 1700 = √((2.89 × 10⁹/rho)) ⇒ 1700² = (2.89 × 10⁹/rho) . rho = (2.89 × 10⁹/1700²) = (2.89 × 10⁹/2.89 × 10⁶) = 1000 kg/m³ . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1000 kg/m³, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Transverse and Longitudinal Waves

A longitudinal wave in a medium has a speed of 1500 m/s and a density of 1200 kg/m³. What is the bulk modulus of the med

**Wave classification** depends on particle vibration relative to propagation. Longitudinal waves have particle oscillation parallel to propagation, creating compressions and rarefactions as in sound in air; transverse have perpendicular oscillation. Tuning fork generates longitudinal sound because air cannot sustain shear. Speed: v = √((B/rho)) . 1500 = √((B/1200)) ⇒ 1500² = (B/1200) . B = 1500² × 1200 = 2.7 × 10⁹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2.7 × 10⁹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.