Sound WavesMedium
Question
Two notes A and B. sounded together, produce 2 beats per sec. Notes B and C sounded together produce 3 beats per sec. The notes A and C separately produce the same number of beats with a standard tuning fork of 456 Hz. The possible frequency of the note B is
Options
A.453.5 Hz
B.453.5 Hz
C.456.5 Hz
D.458.5 Hz
Solution
Let frequency of note B be n then according to question
nA = n - 2 or n + 2
nC = n - 3 or n + 3
As A & C produce same number of beats with T.F. of frequency 456 Hz so
(n - 2) - 456 = 456 - (n - 3) ⇒ n = 458.5 Hz
(n + 3) - 456 = 456 - (n - 2) ⇒ n = 455.5 Hz
(n + 2) - 456 = 456 - (n - 3) ⇒ n = 456.5 Hz
(n + 3) - 456 = 456 - (n + 2) ⇒ n = 453.5 Hz
nA = n - 2 or n + 2
nC = n - 3 or n + 3
As A & C produce same number of beats with T.F. of frequency 456 Hz so
(n - 2) - 456 = 456 - (n - 3) ⇒ n = 458.5 Hz
(n + 3) - 456 = 456 - (n - 2) ⇒ n = 455.5 Hz
(n + 2) - 456 = 456 - (n - 3) ⇒ n = 456.5 Hz
(n + 3) - 456 = 456 - (n + 2) ⇒ n = 453.5 Hz
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