A particular guitar string is supposed to vibrate at 192 Hz, but it is measured to actually vibrate at 212 Hz. By what percent should the tension in the string be changed to get the frequency to the correct value?
To determine the percent change in tension required to achieve the correct frequency, we need to calculate the relative change in frequency and then convert it to a percentage.
The relative change in frequency can be calculated using the formula:
Relative Change in Frequency = (Measured Frequency - Desired Frequency) / Desired Frequency
In this case, the measured frequency is 212 Hz, and the desired frequency is 192 Hz. Plugging these values into the formula:
Relative Change in Frequency = (212 - 192) / 192 = 20 / 192 ≈ 0.1042
Now, to calculate the percent change in tension, we need to convert the relative change in frequency to a percentage by multiplying it by 100:
Percent Change in Tension = Relative Change in Frequency × 100
Percent Change in Tension = 0.1042 × 100 ≈ 10.42%
Therefore, the tension in the guitar string should be adjusted by approximately 10.42% to achieve the correct frequency of 192 Hz.