You have three tuning forks, A, B, and C. Fork B has a frequency of441 Hz; when

Question

You have three tuning forks, A, B, and C. Fork B has a frequency of441 Hz; when A and B are soundedtogether, a beat frequency of 2 Hz isheard. When B and C are sounded together, the beat frequency is4 Hz. What are the possiblefrequencies 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 soundedtogether? lower frequency Hz upper frequency Hz lower frequency Hz upper frequency Hz

Explanation / Answer

   Given frequency of vibration of fork B is fB =461 Hz beat frequency fA - fB = 1Hz beat frequency fB - fC= 4 Hz thus       fA - 461 = 1or fB - fA = 1 Hz so fA = 462 Hz or 460Hz also      fB - fC= 4 Hz or fC -fB = 4Hz         so          fC = 465Hz or 457Hz when A and C are tuned together , the beat frequency is fA - fC = 3Hz or 5Hz Given frequency of vibration of fork B is fB =461 Hz beat frequency fA - fB = 1Hz beat frequency fB - fC= 4 Hz thus       fA - 461 = 1or fB - fA = 1 Hz so fA = 462 Hz or 460Hz also      fB - fC= 4 Hz or fC -fB = 4Hz         so          fC = 465Hz or 457Hz when A and C are tuned together , the beat frequency is fA - fC = 3Hz or 5Hz

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