When a wire under tension is plucked, it vibrates and produces sound waves. The frequency of the sound wave is determined by various factors, including the tension in the wire. If the tension in the wire is increased, the frequency of the sound produced will also change.
To calculate the new frequency when the tension in the wire is increased by 125%, we can use the following formula:
f2 = √(T2 / T1) * f1
Where: f2 is the new frequency, T2 is the new tension in the wire, T1 is the initial tension in the wire and f1 is the initial frequency.
In this case, let’s assume that the initial tension T1 is known and produces a note with a frequency (f1) of 60 Hz. We need to find f2, the new frequency when T2 is increased by 125%.
Using the given information, we have:
f1 = 60 Hz
We need to determine how T2 relates to T1. If T2 is increased by 125%, it can be expressed as:
T2 = T1 + (125 / 100) * T1
T2 = T1 + 125 T1 / 100
T2 = 225 T1 / 100
T2 = 2.25 T1
Substituting these values into the formula, we get:
f2 = √(T2 / T1) * f1
f2 = √(2.25 T1 / T1) * 60 Hz
f2 = √2.25 * 60 Hz
f2 = 1.5 * 60 Hz
f2 = 90 Hz
Therefore, when the tension in the wire is increased by 125%, the frequency of the note produced will be 90 Hz.
