#sound waves

Beats Phenomenon

Two strings produce beats of 8 Hz. One has a frequency of 440 Hz. When the tension in the second string is increased, th

**Beats arise** when two waves of slightly different frequencies f₁ and f₂ superpose, producing amplitude modulation at beat frequency f_beat = |f₁ - f₂| (Hz). Intensity waxes and wanes periodically, number of beats in interval Δt equals f_beat·Δt, loudness variation audible when f_beat < 10 Hz. Let v₂ be the original frequency. |440 - v₂| = 8 ⇒ v₂ = 432 Hz or 448 Hz . Increasing tension increases frequency. If v₂ = 432 , new v₂’ > 432 , beat = 440 - v₂’ < 8 , becomes 6 Hz ( v₂’ = 434 ), consistent. If v₂ = 448 , beat increases, contradicts.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Beats Phenomenon

Two waves of frequencies 480 Hz and 486 Hz interfere. How many beats are heard in 12 seconds?

**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. Beat frequency: vbₑₐt = 486 - 480 = 6 Hz . Beats in 12 s: 6 × 12 = 72 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 72, 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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Superposition and Interference of Waves

Which condition is necessary for the formation of beats between two waves?

**Interference of waves** produces enhancement or cancellation based on phase. Two equal amplitude waves out of phase by π cancel completely, A = 0, while in-phase superposition doubles amplitude to 2a, demonstrating energy redistribution without violation of conservation. Beats require two waves with slightly different frequencies to produce periodic interference, resulting in amplitude modulation. Equal amplitudes or specific wavelengths are not necessary. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Slightly different frequencies, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Superposition and Interference of Waves

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Vibrations of Air Columns - Open and Closed Pipes

A pipe open at both ends has a length of 0.3 m and a speed of sound of 330 m/s. What is the frequency of its second harm

**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. For open pipe: v_n = (n v/2L) . Second harmonic ( n = 2 ): v₂ = (2 × 330/2 × 0.3) = (660/0.6) = 1100 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1100 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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Beats Phenomenon

Two waves of frequencies 512 Hz and 516 Hz interfere. How many beats are heard in 8 seconds?

**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. Beat frequency: vbₑₐt = 516 - 512 = 4 Hz . Beats in 8 s: 4 × 8 = 32 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 32, 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

Two waves of frequencies 450 Hz and 456 Hz produce beats. How many beats are heard in 5 seconds?

**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. Beat frequency: vbₑₐt = 456 - 450 = 6 Hz . Beats in 5 s: 6 × 5 = 30 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 30, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Transverse and Longitudinal Waves

What is the nature of the wave produced by a vibrating tuning fork in air?

**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. A tuning fork vibrates to create compressions and rarefactions in air, producing a longitudinal sound wave, as air cannot sustain transverse oscillations. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Longitudinal, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Transverse and Longitudinal Waves

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