Wave Speed, Energy and Power

Wave Speed, Energy and Power

A transverse wave travels on a string with a tension of 200 N and linear mass density of 0.025 kg/m. What is the wavelen

**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. Speed: v = √((T/μ)) = √((200/0.025)) = √(8000) ≈ 89.4 m/s . Wavelength: λ = (v/v) = (89.4/40) ≈ 2.24 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2.24 m, 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 0.045 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 5 m and mass 0.05 kg is under a tension of 80 N. How long does a transverse pulse take to travel its

**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. Linear mass density: μ = (0.05/5) = 0.01 kg/m . Speed: v = √((T/μ)) = √((80/0.01)) = √(8000) ≈ 89.44 m/s . Time: t = (length/v) = (5/89.44) ≈ 0.056 s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.056 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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Wave Speed, Energy and Power

A transverse wave on a string has a tension of 120 N and a linear mass density of 0.015 kg/m. What is the wavelength if

**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. Speed: v = √((T/μ)) = √((120/0.015)) = √(8000) ≈ 89.44 m/s . Wavelength: λ = (v/v) = (89.44/50) ≈ 1.79 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1.8 m, 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 transverse wave travels on a string with tension 400 N and linear mass density 0.1 kg/m. What is the speed of the wave

**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. Speed: v = √((T/μ)) = √((400/0.1)) = √(4000) ≈ 63.25 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 63.2 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries. This aligns with NCERT Class 11 treatment, emphasizing conservation, symmetry and dimensional consistency useful for CBSE, NEET and CUET.

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

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Wave Speed, Energy and Power

Which property of a sound wave is most directly responsible for its loudness?

**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. Loudness is primarily determined by the amplitude of a sound wave, as it relates to the energy carried and perceived intensity, while frequency affects pitch. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Amplitude, 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 2.8 m and mass 0.07 kg has a fundamental frequency of 35 Hz. What is the tension in the string?

**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. μ = (0.07/2.8) = 0.025 kg/m . v₁ = (v/2L) ⇒ 35 = (v/2 × 2.8) ⇒ v = 35 × 5.6 = 196 m/s . v = √((T/μ)) ⇒ 196 = √((T/0.025)) ⇒ 196² = (T/0.025) . T = 38416 × 0.025 = 960.4 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable,

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

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Wave Speed, Energy and Power

A string of length 2.5 m and mass 0.05 kg has a wave speed of 100 m/s. 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 = (0.05/2.5) = 0.02 kg/m . v = √((T/μ)) ⇒ 100 = √((T/0.02)) ⇒ 100² = (T/0.02) . T = 10000 × 0.02 = 200 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 200 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

A transverse wave on a string has a tension of 200 N and a linear mass density of 0.04 kg/m. What is the wavelength if t

**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. Speed: v = √((T/μ)) = √((200/0.04)) = √(5000) ≈ 70.71 m/s . Wavelength: λ = (v/v) = (70.71/25) ≈ 2.83 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2.83 m, 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 transverse wave on a string has a tension of 90 N and a linear mass density of 0.01 kg/m. What is the frequency if the

**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. Speed: v = √((T/μ)) = √((90/0.01)) = √(9000) ≈ 94.87 m/s . Frequency: v = (v/λ) = (94.87/1.5) ≈ 63.25 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 63 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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