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#mass per length

3 public questions tagged with this topic.

Wave Speed, Energy and Power

A string of length 1.8 m and mass 0.045 kg has a fundamental frequency of 40 Hz. What is the tension in the string?

**Transverse wave velocity** depends on medium not frequency alone. For string under tension, v ∝ √(T/μ), calculation requires μ from mass and length, then square root evaluation, giving v in m/s, then f = v/λ for given wavelength. μ = (0.045/1.8) = 0.025 kg/m . v₁ = (v/2L) ⇒ 40 = (v/2 × 1.8) ⇒ v = 40 × 3.6 = 144 m/s . v = √((T/μ)) ⇒ 144 = √((T/0.025)) ⇒ 144² = (T/0.025) . T = 20736 × 0.025 = 518.4 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 518 N, illustrating

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

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Wave Speed, Energy and Power

A string of length 4 m and mass 0.016 kg is under a tension of 64 N. What is the speed of a transverse wave on the strin

**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 = (0.016/4) = 0.004 kg/m . Speed: v = √((T/μ)) = √((64/0.004)) = √(16000) ≈ 126.5 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 126 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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Wave Speed, Energy and Power

A string of length 1.8 m and mass 0.036 kg has a fundamental frequency of 50 Hz. What is the tension in the string?

**Transverse wave velocity** depends on medium not frequency alone. For string under tension, v ∝ √(T/μ), calculation requires μ from mass and length, then square root evaluation, giving v in m/s, then f = v/λ for given wavelength. μ = (0.036/1.8) = 0.02 kg/m . v₁ = (v/2L) ⇒ 50 = (v/2 × 1.8) ⇒ v = 50 × 3.6 = 180 m/s . v = √((T/μ)) ⇒ 180 = √((T/0.02)) ⇒ 180² = (T/0.02) . T = 32400 × 0.02 = 648 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 648 N, illustrating

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

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