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#string frequency

2 public questions tagged with this topic.

Beats Phenomenon

Two strings produce beats of 6 Hz. One has a frequency of 384 Hz. When the tension in the second string is decreased, 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. |384 - v₂| = 6 ⇒ v₂ = 378 Hz or 390 Hz . Decreasing tension decreases frequency. If v₂ = 390 , new v₂’ < 390 , beat = 390 - 384 = 6 or decreases, so v₂’ = 380 , beat = 384 - 380 = 4 , consistent. Thus, v₂

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Stationary Waves and Standing Waves in Strings

A string fixed at both ends has a length of 1.6 m and a wave speed of 80 m/s. What is the frequency of its first harmoni

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. For fixed ends: v_n = (n v/2L) . First harmonic ( n = 1 ): v₁ = (80/2 × 1.6) = (80/3.2) = 25 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 25 Hz, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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