You have three tuning forks, A, B, and C. Fork B has a frequency of461 Hz; when

Question

You have three tuning forks, A, B, and C. Fork B has a frequency of461 Hz; when A and B are soundedtogether, a beat frequency of 1 Hz isheard. When B and C are sounded together, the beat frequency is4 Hz. What are the possiblefrequencies of A? lower frequency 1 Hz upper frequency 2 Hz
What are the possible frequencies of fork C? lower frequency 3 Hz upper frequency 4 Hz
What beat frequencies are possible when A and C are soundedtogether? lower frequency 5 Hz upper frequency 6 Hz lower frequency 1 Hz upper frequency 2 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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