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#wave speed

76 public questions tagged with this topic.

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 of length 2 m and mass 0.01 kg is under a tension of 100 N. What is the time taken by a transverse pulse to tra

**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. Linear mass density: μ = (mass/length) = (0.01/2) = 0.005 kg/m . Speed: v = √((T/μ)) = √((100/0.005)) = √(20000) ≈ 141.4 m/s . Time: t = (length/v) = (2/141.4) ≈ 0.014 s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.014 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 of length 2.2 m fixed at both ends has a wave speed of 66 m/s. What is the frequency of its fourth harmonic?

**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. v_n = (n v/2L) . Fourth harmonic ( n = 4 ): v₄ = (4 × 66/2 × 2.2) = (264/4.4) = 60 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 60 Hz, 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 1.4 m and a wave speed of 70 m/s. What is the frequency of its second harmon

**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. For fixed ends: v_n = (n v/2L) . Second harmonic ( n = 2 ): v₂ = (2 × 70/2 × 1.4) = (140/2.8) = 50 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 50 Hz, 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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Doppler Effect

A string of length 3 m and mass 0.06 kg is under a tension of 150 N. What is the speed of a transverse wave on the strin

**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. Linear mass density: μ = (0.06/3) = 0.02 kg/m . Speed: v = √((T/μ)) = √((150/0.02)) = √(7500) ≈ 86.6 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 86.6 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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Doppler Effect

A string of length 4 m and mass 0.08 kg is under a tension of 200 N. How long does a transverse pulse take to travel its

**Doppler effect** describes apparent frequency shift due to relative motion between source and observer, f' = f·v/(v ∓ v_s) for source motion, f' = f·(v ± v_o)/v for observer motion, upper signs for approach increasing observed frequency. Motion towards observer compresses wavelength raising f'. Linear mass density: μ = (0.08/4) = 0.02 kg/m . Speed: v = √((T/μ)) = √((200/0.02)) = √(10000) = 100 m/s . Time: t = (length/v) = (4/100) = 0.04 s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.04 s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Doppler Effect

A stationary wave on a string fixed at both ends has a frequency of 150 Hz and a wave speed of 45 m/s. What is the wavel

**Doppler effect** describes apparent frequency shift due to relative motion between source and observer, f' = f·v/(v ∓ v_s) for source motion, f' = f·(v ± v_o)/v for observer motion, upper signs for approach increasing observed frequency. Motion towards observer compresses wavelength raising f'. Wavelength: λ = (v/v) = (45/150) = 0.3 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.3 m, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Doppler Effect

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Beats Phenomenon

A string of length 2.4 m fixed at both ends has a wave speed of 72 m/s. What is the frequency of its fifth harmonic?

**Superposition of nearly equal frequencies** creates resultant y = 2A cos(Δω·t/2) sin(ω_avg·t), envelope frequency Δf/2, beat frequency Δf. Total beats heard in Δt is f_beat·Δt, explaining counting over seconds. v_n = (n v/2L) . Fifth harmonic ( n = 5 ): v₅ = (5 × 72/2 × 2.4) = (360/4.8) = 75 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 75 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Beats Phenomenon

A stationary wave on a string fixed at both ends has a wavelength of 0.6 m and a frequency of 100 Hz. What is the wave s

**Superposition of nearly equal frequencies** creates resultant y = 2A cos(Δω·t/2) sin(ω_avg·t), envelope frequency Δf/2, beat frequency Δf. Total beats heard in Δt is f_beat·Δt, explaining counting over seconds. Speed: v = v λ = 100 × 0.6 = 60 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 60 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 > Beats Phenomenon

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Beats Phenomenon

A transverse wave on a string has a speed of 18 m/s and a frequency of 6 Hz. What is its wavelength?

**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. Speed: v = v λ . Wavelength: λ = (v/v) = (18/6) = 3 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3 m, 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 > Beats Phenomenon

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