Physics Help-Waves: You have three tuning forks, A, B, and C. Fork B has a frequency of 461 Hz; when A and B are sounded

[405]

You have three tuning forks, A, B, and C. Fork B has a frequency of 461 Hz; when A and B are sounded together, a beat frequency of 2 Hz is heard. When B and C are sounded together, the beat frequency is 7 Hz. What are the possible frequencies of A?
lower frequency Hz
upper frequency Hz

What are the possible frequencies of fork C?
lower frequency Hz
upper frequency Hz

What beat frequencies are possible when A and C are sounded together?
lower frequency Hz
upper frequency Hz

[Woodsman]

| fa - fb | = fab
| fa - 461 | = 2
→ fa = 459 Hz, 463 Hz

| fc - fb | = fbc
| fc - 461 | = 7
→ fc = 454 Hz, 468 Hz

Possible beat frequencies for A and C are
468 - 459 = 9 Hz }
468 - 463 = 5 Hz } → So the possible beat frequencies are
463 - 454 = 9 Hz } → 5 Hz and 9 Hz, or 7 Hz ± 2 Hz
459 - 454 = 5 Hz }