#wave mechanics

Sound Waves, Reflection and Characteristics

A pipe open at both ends has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fourth harm

**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. For open pipe: v_n = (n v/2L) . Fourth harmonic ( n = 4 ): v₄ = (4 × 320/2 × 0.4) = (1280/0.8) = 1600 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1600 Hz, 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

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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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.

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

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Transverse and Longitudinal Waves

What is the primary source of restoring force for transverse waves on a stretched string?

**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. In transverse waves on a string, the tension provides the restoring force that opposes displacement, enabling wave propagation, unlike elasticity or pressure in other contexts. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Tension, 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

A string of length 3.2 m and mass 0.064 kg has a fundamental frequency of 25 Hz. What is the tension in the string?

**Energy transport** in waves scales with amplitude squared A² and frequency squared ω². Wave speed determines propagation rate, and understanding T and μ allows quantitative prediction of v and associated frequencies. μ = (0.064/3.2) = 0.02 kg/m . v₁ = (v/2L) ⇒ 25 = (v/2 × 3.2) ⇒ v = 25 × 6.4 = 160 m/s . v = √((T/μ)) ⇒ 160 = √((T/0.02)) ⇒ 160² = (T/0.02) . T = 25600 × 0.02 = 512 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 512 N, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Wave Speed, Energy and Power

What happens to the speed of a transverse wave on a string if the tension is doubled while keeping the linear mass densi

**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. The speed of a transverse wave is v = √((T/μ)) . If tension T doubles, v' = √((2T/μ)) = √(2) × v , increasing by a factor of √(2) (approximately 1.414). Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Increases by a factor of √(2), illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Wave Speed, Energy and Power

A string of length 2.4 m and mass 0.048 kg is under a tension of 300 N. What is the speed of a transverse wave on the st

**Energy transport** in waves scales with amplitude squared A² and frequency squared ω². Wave speed determines propagation rate, and understanding T and μ allows quantitative prediction of v and associated frequencies. Linear mass density: μ = (0.048/2.4) = 0.02 kg/m . Speed: v = √((T/μ)) = √((300/0.02)) = √(15000) ≈ 122.47 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 122.5 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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