91影视

The string鈥檚 fundamental frequency can be obtained by the ratio of the whole square root of the string鈥檚 tension and linear density to twice the string鈥檚 length.

Given data:

The frequency of two violin strings is \(f = 294\;{\rm{Hz}}\).

When the tension in one string is decreased by \(2.5\% \), the new tension in the string can be calculated as:

\(\begin{array}{c}{{F'}_T} = \left( {1 - \frac{{2.5}}{{100}}} \right){F_T}\\{{F'}_T} = 0.975{F_T}\end{array}\)

The new fundamental frequency of the string can be given as:

\(f' = \frac{1}{{2L}}\sqrt {\frac{{{{F'}_T}}}{\mu }} \) 鈥� (1)

After substituting the given values in equation (1), you get:

\(\begin{array}{c}f' = \frac{1}{{2L}}\sqrt {\frac{{0.975{F_T}}}{\mu }} \\f' = \sqrt {0.975} \left[ {\frac{1}{{2L}}\sqrt {\frac{{{F_T}}}{\mu }} } \right]\\f' = \sqrt {0.975} f\\f' = \sqrt {0.975} \times \left( {294\;{\rm{Hz}}} \right)\\f' = 290.30\;{\rm{Hz}}\end{array}\)

The beat frequency can be calculated as:

\(\begin{array}{c}{f_B} = \left| {f - f'} \right|\\{f_B} = \left| {294\;{\rm{Hz}} - 290.30\;{\rm{Hz}}} \right|\\{f_B} = 3.7\;{\rm{Hz}}\end{array}\)

Thus, when the two strings are played together, the beat frequency will be \(3.7\;{\rm{Hz}}\).