Question

You have three tuning forks, A, B, and C. Fork B has a frequency of 421 Hz; when A and B are sounded together, a beat frequency of 1 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

Answer 1

a] Beat frequency = difference in frequencies

here, for A and B

Beat frequency = 1 Hz

so, frequency of A can be either 422 Hz or 420 Hz

upper frequency of A will, therefore, be 422 Hz and lower frequency will be 420 Hz.

b] Similarly, beat frequency for B and C is 7 Hz

so, Frequency of C can be either: 421+7 = 429 Hz or 421-7 = 414 Hz

therefore, upper frequency of C is: 429 Hz and lower frequency is 414 Hz

c]

Frequencies of A = 420 Hz, 422 Hz

Frequencies of C = 414 Hz,429 Hz

so, the beat frequencies of A and C will be:

i] 420 - 414 = 6 Hz

ii] 422 - 414 = 8 Hz

iii] 429 - 422 = 7 Hz

iv] 429 - 420 = 9 Hz

so, the upper frequency is 9 Hz and lower frequency is 6 Hz.