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Practice question

Question

Two sitar strings produce beats of 5 Hz. If one has a frequency of 320 Hz and tension in the other is
reduced, the beat frequency increases to 7 Hz. What is the original frequency of the second string?

Options

Choose one · Correct answer highlighted

Explanation

**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. |320 - v₂| = 5 ⇒ v₂ = 315 Hz or 325 Hz . Reducing tension decreases frequency. If v₂ = 325 , new v₂’ < 325 , beat = 325 - 320 = 5 or increases, so v₂’ = 313 , beat = 320 - 313 = 7 , consistent. Thus, v₂ = 325 Hz . Using v = fλ and standing-wave condition

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