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#tension change

2 public questions tagged with this topic.

Beats Phenomenon

Two strings produce beats of 4 Hz. If one has a frequency of 256 Hz and the tension in the other is increased, the beat

**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. Let original frequency of second string = v₂ . |256 - v₂| = 4 ⇒ v₂ = 252 Hz or 260 Hz . Tension increase raises frequency. If v₂ = 252 , new v₂ > 252 , beat = 256 - v₂’ < 4 , contradicts. If v₂ = 260 , new v₂ > 260 , beat = v₂’ - 256 = 6 ⇒ v₂’ = 262 Hz , consistent. So, v₂ = 260 Hz .

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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Beats Phenomenon

Two strings produce beats of 6 Hz. One has a frequency of 300 Hz. When the tension in the second string is decreased, th

**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. Let v₂ be the original frequency. |300 - v₂| = 6 ⇒ v₂ = 294 Hz or 306 Hz . Decreasing tension decreases frequency. If v₂ = 306 , new v₂’ < 306 , beat = 306 - 300 = 6 or decreases, so v₂’ = 296 , beat = 300 - 296 = 4 , consistent. Thus, v₂ = 306 Hz . Using v = fλ and standing-wave condition

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

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