Two identical violin strings, when in true and stretched with same tension , have a fundamental frequency of `440.0 H_(Z)`. One of the string is retuned by adjusting its tension . When this is done, `1.5` beats per second are heard when both strings are plucked simultaneously. (a) What are the possible fundamental frequencies of the retuned string? (b) by what fractional amount was the string tension changed if it was (i) increased (ii) decreased?

Answer

A, B, C, D

Explanation

(a) Possing fundamental frequcies of retuned string is `(440 +- 1.5) H_(Z)` (b) `f prop sqrt(T)`
:. `(f_(1))/(f_(2)) = sqrt(T_(1)/(T_(2)))`
:. `T_(2) = ((f_(2))/(f_(1))^(2)) T_(1)` (i) `T_(2) = ((441.5)/(440))^(2)`
`T_(1) = 1.0068 T_(1)`
% change ` = (T_(2) - T_(1))/(T_(1)) xx 100`
` = + 0.68%` (ii) `T_(2) = ((438.5)/(440))^(2) T_(1) = 0.9932 T_(1)`
` %` change `= (T_(2) - T_(1))/(T_(1)) xx 100`
` = - 0.68%`