The frequency obtained from a plucked string when the extension is 2newton is 400hz . calculate frequency when the extension is increased by 6newton?

To calculate the frequency when the extension is increased by 6 newtons, we can use the formula:

f = (1/2L) * sqrt(T/μ)

Where:
f = frequency
L = length of the string
T = tension in the string
μ = mass per unit length of the string

Given that the frequency obtained when the extension is 2 newtons is 400 Hz, we can calculate the initial tension in the string using the formula:

T = k * x

Where:
k = spring constant
x = extension

Given that the extension is 2 newtons and the frequency is 400 Hz, we can calculate the initial tension:

T = k * 2

Now, we can calculate the initial tension using the formula:

400 = (1/2L) * sqrt(T/μ)

Now, we can calculate the new frequency when the extension is increased by 6 newtons:

T_new = k * (2 + 6)

f_new = (1/2L) * sqrt(T_new/μ)

f_new = (1/2L) * sqrt(8k/μ)

Therefore, the new frequency when the extension is increased by 6 newtons is:

f_new = 400 * sqrt(8/2) = 400 * sqrt(4) = 400 * 2 = 800 Hz.