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Tuning fork B has frequency 441 Hz. When forks A and B are sounded together, 3 beats per second are heard. When forks B and C are sounded together, 4 beats per second are heard. Which of the following statements are correct? (A) The frequency of A can be 438 Hz. (B) The frequency of C can be 444 Hz. (C) The beat frequency between A and C can be 1 Hz. (D) The beat frequency between A and C can be 6 Hz.

1. (A) The frequency of A can be 438 Hz.
2. (B) The frequency of C can be 444 Hz.
3. (C) The beat frequency between A and C can be 1 Hz.
4. (D) The beat frequency between A and C can be 6 Hz.

Correct answer: (D) The beat frequency between A and C can be 6 Hz.

Solution

Frequency of A: |f_A - 441| = 3, so f_A = 438 or 444 Hz. Frequency of C: |f_C - 441| = 4, so f_C = 437 or 445 Hz. Possible beat frequencies between A and C: |438 - 437| = 1 Hz, |438 - 445| = 7 Hz, |444 - 437| = 7 Hz, |444 - 445| = 1 Hz. So possible beat frequencies are 1 Hz and 7 Hz. Statement A: f_A = 438 is possible. TRUE. Statement B: f_C = 444 is NOT possible (C must be 437 or 445). FALSE. Statement C: beat = 1 Hz is possible. TRUE. Statement D: beat = 6 Hz is NOT achievable. FALSE. Correct statements are A and C.

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