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#fundamental frequency

18 public questions tagged with this topic.

Sound Waves, Reflection and Characteristics

A steel rod of length 2 m has a fundamental frequency of longitudinal vibrations of 1.25 kHz. What is the speed of sound

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 1250 = (v/2 × 2) ⇒ v = 1250 × 4 = 5000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 5000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Doppler Effect

A string fixed at both ends has a length of 1.6 m and a fundamental frequency of 62.5 Hz. What is the speed of the wave?

**Relative motion** changes effective wavelength encountered. For moving source approaching stationary observer, wavelength ahead λ' = (v - v_s)/f, so f' = v/λ' = f·v/(v - v_s) > f, basis for calculating apparent pitch shift in sound. Fundamental: v₁ = (v/2L) . 62.5 = (v/2 × 1.6) ⇒ v = 62.5 × 3.2 = 200 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 200 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Doppler Effect

A string fixed at both ends has a length of 1.5 m and a fundamental frequency of 50 Hz. What is the speed of the wave on

**Frequency shift** proportional to source speed relative to wave speed v. Understanding sign convention for approaching versus receding is key, with approaching increasing frequency and receding decreasing, central to Doppler applications. Fundamental frequency: v₁ = (v/2L) . 50 = (v/2 × 1.5) ⇒ 50 = (v/3) ⇒ v = 150 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 150 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Sound Waves, Reflection and Characteristics

A steel rod of length 1.5 m has a fundamental frequency of longitudinal vibrations of 2 kHz. What is the speed of sound

**Longitudinal vibrations in rods** clamped at middle have fundamental with node at clamp and antinodes at ends, f₁ = v/(2L), v speed of sound in material (m/s). This relation allows v extraction from measured f₁ and length L, e.g., v = 2L·f₁. For rod clamped at middle, fundamental: v₁ = (v/2L) . 2000 = (v/2 × 1.5) ⇒ v = 2000 × 3 = 6000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 6000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Beats Phenomenon

A string of length 2.5 m and mass 0.025 kg has a fundamental frequency of 40 Hz. What is the tension in the string?

**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. μ = (0.025/2.5) = 0.01 kg/m . v₁ = (v/2L) ⇒ 40 = (v/2 × 2.5) ⇒ v = 40 × 5 = 200 m/s . v = √((T/μ)) ⇒ 200 = √((T/0.01)) ⇒ 200² = (T/0.01) . T = 40000 × 0.01 = 400 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 400 N, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Sound Waves, Reflection and Characteristics

A pipe closed at one end has a length of 0.4 m and a speed of sound of 320 m/s. What is the frequency of its fundamental

**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. Fundamental: v₁ = (v/4L) . v₁ = (320/4 × 0.4) = (320/1.6) = 200 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 200 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

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

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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.35 m and resonates at its fundamental frequency with a speed of sound of 350

**Air column vibrations** depend on end conditions. Pipe closed at one end has displacement node at closed end and antinode at open, allowing only odd harmonics, fundamental f₁ = v/(4L). Open pipe has antinodes at both ends, fₙ = n·v/(2L), all harmonics present, v sound speed. Fundamental: v₁ = (v/4L) . v₁ = (350/4 × 0.35) = (350/1.4) = 250 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 250 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Vibrations of Air Columns - Open and Closed Pipes

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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.5 m and resonates at its fundamental frequency with a speed of sound of 350 m

**Organ pipe modes** illustrate boundary influence. Closed pipe odd harmonic series contrasts with open pipe full series, affecting timbre. Frequency scales inversely with length, explaining pitch variation with pipe length. Fundamental: v₁ = (v/4L) . v₁ = (350/4 × 0.5) = (350/2) = 175 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 175 Hz, 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 > Vibrations of Air Columns - Open and Closed Pipes

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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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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.5 m and a speed of sound of 340 m/s. What is the frequency of its fundamental

**Resonance in pipes** occurs when length accommodates standing wave pattern. Closed pipe L = (2n-1)λ/4, so f₁ = v/(4L). Given f₁ and v, length follows L = v/(4f₁), enabling length calculation from measured resonance frequency and sound speed 330-340 m/s. Fundamental: v₁ = (v/4L) . v₁ = (340/4 × 0.5) = (340/2) = 170 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 170 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Vibrations of Air Columns - Open and Closed Pipes

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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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Vibrations of Air Columns - Open and Closed Pipes

A pipe closed at one end has a length of 0.25 m and resonates at its fundamental frequency with a speed of sound of 340

**Resonance in pipes** occurs when length accommodates standing wave pattern. Closed pipe L = (2n-1)λ/4, so f₁ = v/(4L). Given f₁ and v, length follows L = v/(4f₁), enabling length calculation from measured resonance frequency and sound speed 330-340 m/s. Fundamental: v₁ = (v/4L) . v₁ = (340/4 × 0.25) = (340/1) = 340 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 340 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Vibrations of Air Columns - Open and Closed Pipes

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