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#rigid boundary

6 public questions tagged with this topic.

Sound Waves, Reflection and Characteristics

A wave \( y = 0.07 \sin (20x - 60t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

**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 rigid boundary, phase changes by π . Incident: y_i = 0.07 sin (20x - 60t) . Reflected: y_r = -0.07 sin (20x + 60t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.07 sin (20x + 60t), illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Transverse and Longitudinal Waves

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

**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. 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. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0 radians, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Sound Waves, Reflection and Characteristics

A wave \( y = 0.05 \sin (12x - 36t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

**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. At rigid boundary, phase changes by π . Incident: y_i = 0.05 sin (12x - 36t) . Reflected: y_r = -0.05 sin (12x + 36t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.05 sin (12x + 36t), illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Wave Equation and Displacement Relation

A travelling wave is reflected at a rigid boundary. If the incident wave is \( y = 0.05 \sin (10x - 20t) \), what is the

**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 rigid boundary, phase changes by π . Incident: y_i = 0.05 sin (10x - 20t) . Reflected: y_r = -0.05 sin (10x + 20t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.05 sin (10x + 20t), 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

A wave \( y = 0.07 \sin (25x - 50t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

**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. At rigid boundary, phase changes by π . Incident: y_i = 0.07 sin (25x - 50t) . Reflected: y_r = -0.07 sin (25x + 50t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.07 sin (25x + 50t), 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 wave \( y = 0.08 \sin (10x - 30t) \) reflects at a rigid boundary. What is the equation of the reflected wave?

**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 rigid boundary, phase changes by π . Incident: y_i = 0.08 sin (10x - 30t) . Reflected: y_r = -0.08 sin (10x + 30t) . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields y = -0.08 sin (10x + 30t), illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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