A particular guitar string is supposed to vibrate at 210Hz , but it is measured to vibrate at 220Hz

By what percent should the tension in the string be changed to correct the frequency?

Instead of subtracting 1 at the end, I divided the result by 1 and then subtracted from 1.

1 - (1 / (220/210)²) = 8.89%

Well, if the tension in the string is making it vibrate at the wrong frequency, then it's time for a string intervention! To calculate the percentage change needed to correct the frequency, we can use the formula:

Percentage Change = (New Value - Original Value) / Original Value * 100

In this case, the original frequency is 210Hz and the new frequency is 220Hz. Plugging these values into the formula, we get:

Percentage Change = (220 - 210) / 210 * 100

Calculating it out, we find that the tension in the string needs to be changed by approximately 4.76% to correct the frequency. So, it's time to give that string a little tension adjustment, just like your mood after a good joke!

To calculate the percent change in tension needed to correct the frequency, we can use the formula for percent change:

Percent change = (new value - old value) / old value × 100

In this case, the old frequency is 210Hz and the new frequency is 220Hz.

Percent change = (220Hz - 210Hz) / 210Hz × 100

Percent change = 10Hz / 210Hz × 100

Percent change ≈ 0.0476 × 100

Percent change ≈ 4.76%

Therefore, the tension in the guitar string should be changed by approximately 4.76% to correct the frequency.

To determine the percentage change in tension required to correct the frequency of the guitar string, we can use the formula:

Percentage change = ((New Value - Original Value) / Original Value) * 100

In this case, the original frequency is 210Hz, and the new measured frequency is 220Hz. We need to find the percentage change in tension that would correct this difference.

Using the formula, we can calculate the percentage change as follows:

Percentage change = ((220 - 210) / 210) * 100

Simplifying the equation gives:

Percentage change = (10 / 210) * 100

To calculate the actual value:

Percentage change = 0.0476 * 100

So, the tension in the string should be changed by approximately 4.76% to correct the frequency.

v=sqrt(T•L/m)

λ=v/f => f=v/λ= sqrt(T•L/m)/ λ
f₁/f₂={sqrt(T₁•L/m)/ λ}/{sqrt(T₂•L/m)/ λ}
(f₁/f₂)² =T₁/T₂
T₂=T₁(f₂/f₁)²
(T₂-T₁)/T₁=(T₂/T₁) -1=(f₂/f₁)²-1=(220/210)²-1=0.0975.
=> 9.75%