A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec. when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

A tuning fork of frequency 512 Hz makes 4 beats per second with the vi

1.	A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec. when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
Answer» (A) 510 Hz (B) 514 Hz (C) 516 Hz (D) 508 Hz Solution :For TUNING fork `f _(A) =512 Hz` For piano wire, `f _(B) = 516 OR 508 Hz ` `(because ` Initially beat frequency is 4 beat/second) When tension is increased in piano wire, new beat frequency `f _(A) - f._(B)` becomes 2 Hz. When tension in increased, frequency of piano wire increase. Hence `f ._(B) gt f _(B)` Moreover `f _(A) - f._(B) =2 ` `therefore f _(B) = 508 Hz and f._(B) = 510 Hz` So that `(i) f _(A) - f _(B) = 512 - 508 = 2 Hz` As per the statement, Thus, `f _(B) = 508 Hz` Note Here `f _(B) ne 516 ` because `f ._(B) gt f _(B)` and so `f ._(B) -f_(A) gt 4 Hz` which would be WRONG as it is not so in the statement.