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#string wave

5 public questions tagged with this topic.

Beats Phenomenon

A stationary wave on a string is given by \( y = 0.08 \sin (2\pi x) \cos (100\pi t) \), where \( x \) and \( y \) are in

**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. Form: y = A sin (kx) cos (ω t) , k = 2π rad/m . Wavelength: λ = (2π/k) = (2π/2π) = 1 m . Distance between nodes: (λ/2) = (1/2) = 0.5 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.5 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Transverse and Longitudinal Waves

A wave on a string has an amplitude of 0.025 m and a frequency of 50 Hz. What is the maximum transverse speed of a parti

**Mechanical waves** require medium and can be transverse or longitudinal. Sound in air is longitudinal since fluids support only compressional motion, while string waves are transverse. Progressive waves transfer energy without net mass transport, distinguishing from standing waves. ω = 2π v = 2π × 50 = 100π rad/s . Max speed: vₘₐₓ = a ω = 0.025 × 100π ≈ 7.85 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 7.85 m/s, 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

A wave on a string has an amplitude of 0.04 m and a period of 0.02 s. What is the maximum transverse speed of a particle

**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. ω = (2π/T) = (2π/0.02) = 100π rad/s . Max speed: vₘₐₓ = a ω = 0.04 × 100π ≈ 12.56 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 12.6 m/s, illustrating frequency-length-speed interdependence and quantization by bound

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

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Transverse and Longitudinal Waves

A wave on a string has an amplitude of 0.035 m and a frequency of 20 Hz. What is the maximum transverse speed of a parti

**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. ω = 2π v = 2π × 20 = 40π rad/s . Max speed: vₘₐₓ = a ω = 0.035 × 40π ≈ 4.4 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 4.4 m/s, 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

A wave on a string has an amplitude of 0.06 m and a frequency of 30 Hz. What is the maximum transverse acceleration of a

**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. ω = 2π v = 2π × 30 = 60π rad/s . Max acceleration: aₘₐₓ = a ω² = 0.06 × (60π)² . aₘₐₓ = 0.06 × 3600π² ≈ 21330 m/s² . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 21330 m/s², illustrating frequency-length-speed interdepen

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

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