#wave frequency

Wave Equation and Displacement Relation

A wave is described by \( y(x, t) = 0.01 \sin (40x - 80t) \), where \( x \) and \( y \) are in meters and \( t \) in sec

**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. Compare with y = a sin (kx - ω t) , ω = 80 rad/s . Frequency: v = (ω/2π) = (80/2π) ≈ 12.73 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 13 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Beats Phenomenon

Two strings produce beats of 3 Hz. One has a frequency of 288 Hz. When the tension in the second string is increased, th

**Beat formation** is interference in time with time-varying amplitude. Frequencies close together generate slow modulation, count in given duration obtained by multiplying beat frequency by duration, e.g., 6 Hz × 5 s = 30 beats. Let v₂ be the original frequency. |288 - v₂| = 3 ⇒ v₂ = 285 Hz or 291 Hz . Increasing tension increases frequency. If v₂ = 285 , new v₂’ > 285 , beat = 288 - v₂’ < 3 , becomes 1 Hz ( v₂’ = 287 ), consistent. If v₂ = 291 , beat increases, contradicts. So, v₂ = 285 Hz . Using v = fλ and

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Wave Equation and Displacement Relation

A wave is described by \( y(x, t) = 0.03 \sin (50x - 200t) \), where \( x \) and \( y \) are in meters and \( t \) in se

**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. Compare with y = a sin (kx - ω t) . ω = 200 rad/s . Frequency: v = (ω/2π) = (200/2π) ≈ 31.8 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 32 Hz, 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 wave is described by \( y(x, t) = 0.06 \sin (15x - 45t) \), where \( x \) and \( y \) are in meters and \( t \) in sec

**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. Compare with y = a sin (kx - ω t) , ω = 45 rad/s . Frequency: v = (ω/2π) = (45/2π) ≈ 7.16 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 7.2 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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