#wave reflection

What happens to the wavelength of a wave when it reflects off a free end without changing the medium?

**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. Reflection at a free end does not alter the medium’s properties (tension, density), so the wave speed and frequency remain unchanged, keeping the wavelength constant ( λ = v/f ). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields It 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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Wave Equation and Displacement Relation

What happens to a transverse wave when it reflects off a fixed end of a string?

**Displacement relation** encodes λ = 2π/k and f = ω/2π. Comparing given equation y = a sin(kx - ωt) with standard form yields k and ω, hence λ = 2π/k and v = ω/k, essential for identifying propagation characteristics and phase. At a fixed end, the displacement must be zero, requiring the reflected wave to be out of phase by π radians (inverted) to cancel the incident wave at the boundary. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields It reflects with a phase change of π radians, 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

What is the primary physical quantity that remains constant for a wave reflecting off a boundary within the same medium?

**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. Reflection within the same medium preserves the wave’s frequency, as it depends on the source, while speed, wavelength, and amplitude may adjust based on boundary conditions. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Frequency, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Sound Waves, Reflection and Characteristics

Why does a wave reflect with no phase change at a free end?

**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. At a free end, the boundary is unconstrained, allowing maximum displacement. The reflected wave reinforces the incident wave in the same direction, maintaining phase. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Due to maximum displacement, illustrating frequency-length-speed interdependence and quantization by boundaries.