Question

Each of three tuning forks, A, B, and C, has a slightly different frequency. When A and B are sounded together, they produce a beat frequency of 2 Hz. When A and C are sounded together, they produce a beat frequency of 5 Hz. What is the smallest possible beat frequency when B and C are sounded together

Answer 1

Answer:

The smallest possible beat frequency when B and C are sounded together is 3 Hz

Explanation:

Given;

the beat frequency of A and B = 2 Hz

the beat frequency of A and C = 5 Hz

Beat frequency is equal to the difference in frequency of the two notes that interfere to produce the beats.

$F_b_{(AB)} = 2 \ Hz\\\\F_A - F_B = 2 \ Hz -----equation(1)\\\\F_b_{(AC)} = 5 \ Hz\\\\F_A - F_C = 5 \ Hz-----equation(2)\\\\from \ equation(1), make \ F_A \ the \ subject \ of \ the \ formula\\\\F_A = 2H_z + F_B -----equation (3)\\\\Substitute \ in \ the \ value \ of \ F_A \ in \ equation(3) \ into \ equation(2)\\\\2H_z + F_B - F_C = 5H_z\\\\F_B-F_C = 5H_z - 2H_z\\\\F_B -F_C = 3Hz$

Therefore, the smallest possible beat frequency when B and C are sounded together is 3 Hz