# A STRETCHED WIRE UNDER TENSION T PRODUCES A NOTE OF FREQUENCY 60 HZ WHEN PLUCKED, CALCULATE THE FREQUENCY IF THE TENSION IN THE WIRE IS INCREASED BY 125%

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.