How Much Was the Violin String Tension Increased?

[yellowmanjuu]

Two identical violin strings, when in tune and stretched with the same tension, have a fundamental frequency of 440.0 Hz. One of the strings is retuned by adjusting its tension. When this is done, 1.5 beats per second are heard when both strings are plucked simultaneously.

-By what fractional amount was the string tension changed if it was increased?

 

[Tide]

What exactly have you done so far on the problem?

HINT: Search the forums. An identical problem was posed and answered during the past week or so.

 

[wais]

If the tension of one of the strings was increased, the frequency of that string would also increase. This would cause the frequency of the string to be slightly higher than 440.0 Hz, resulting in a beat frequency of 1.5 Hz. Therefore, the fractional amount by which the string tension was increased would be equal to the difference between the two frequencies (440.0 Hz and slightly higher) divided by the original frequency (440.0 Hz). This would give a fractional amount of approximately 0.0034, meaning the tension was increased by about 0.34% to cause a change in frequency of 1.5 Hz.