#longitudinal waves

Doppler Effect

Which property of a medium is most critical for the propagation of longitudinal waves through a gas?

**Relative motion** changes effective wavelength encountered. For moving source approaching stationary observer, wavelength ahead λ' = (v - v_s)/f, so f' = v/λ' = f·v/(v - v_s) > f, basis for calculating apparent pitch shift in sound. Longitudinal waves in a gas rely on compressibility, quantified by the bulk modulus, which provides the restoring force for pressure oscillations, unlike shear modulus needed for transverse waves. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Bulk modulus, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Transverse and Longitudinal Waves

Which property of a medium allows longitudinal waves to propagate through it but not transverse waves?

**Nature of wave** determines energy transfer mechanism. Longitudinal nature of sound explains propagation through fluids with density variations carrying energy, unlike transverse waves needing rigidity for restoring force. Longitudinal waves require a medium with bulk modulus (resistance to compression), which fluids possess. Transverse waves need shear modulus (resistance to shearing), which fluids lack due to their inability to sustain shear stress. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Lack of shear modulus, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Transverse and Longitudinal Waves

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Transverse and Longitudinal Waves

What is the key requirement for a medium to support both transverse and longitudinal waves?

**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. A medium must be rigid (have shear modulus) to support transverse waves and compressible (have bulk modulus) for longitudinal waves, properties typical of solids. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Rigidity, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Transverse and Longitudinal Waves

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Wave Speed, Energy and Power

Which property of a gas affects the speed of longitudinal waves more significantly than its density?

**Wave speed on string** is v = √(T/μ), T tension (N), μ = m/L linear mass density (kg/m). Higher T increases restoring force raising speed, heavier μ lowers speed. Frequency follows f = v/λ, linking mechanical properties to wave dynamics and harmonic series. Speed of sound in a gas is v = √((gamma P/rho)) . The ratio gamma (specific heats) influences v more than rho alone, as P/rho relates to temperature, but gamma varies with molecular structure. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Ratio of specific heats, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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PHYSICS

What is the phase change when a longitudinal wave reflects off a rigid boundary?

For a longitudinal wave, a rigid boundary (fixed end) causes a compression to reflect as a compression, resulting in no phase change (0 radians), unlike transverse waves which invert.

Ref: NCERT Physics Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII, continuing as per NCERT advisory for 2026-27),Topic: Fundamental laws, definitions and applications as per latest NCERT. The section explains governing laws, formulas like μ₀ = 4π.

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