One of the 79.0 -long strings of an ordinary guitar is tuned to produce the note (frequency 245 ) when vibrating in its fundamental mode.
Part A- If the tension in this string is increased by 3.2 , what will be the new fundamental frequency of the string?
F= ? Hz
i understood the other parts of the question except the part A please help thanks
frequency goes up as the square root of tension.
what is sqrt(3.2) * 245hz?
its wrong :/
To find the new fundamental frequency of the string, we need to use the formula for the frequency of a vibrating string:
f = (1/2L) * sqrt(T/μ)
Where:
f = frequency
L = length of the string
T = tension in the string
μ = linear mass density of the string
In this case, the length of the string (L) is given as 79.0 cm, the tension (T) in the string is increased by 3.2 N, and we need to find the new frequency (f).
To find the linear mass density (μ) of the string, we can divide the mass of the string by its length:
μ = mass / length
Unfortunately, the mass of the string is not given in the question. So, we need additional information to calculate the new frequency accurately.
If we assume that the linear mass density (μ) remains constant even after the increase in tension, we can proceed with the calculation. In a real scenario, the mass density of the string might change due to the tension increase, but for the sake of this calculation, let's assume it remains constant.
Now, let's plug in the given values into the formula and solve for the new frequency (f):
f_new = (1/2 * L) * sqrt((T + ΔT) / μ)
Where:
ΔT = change in tension
In this case, ΔT = 3.2 N.
f_new = (1/2 * 79.0 cm) * sqrt((T + 3.2 N) / μ)
Converting the length to meters (1 cm = 0.01 m), the formula becomes:
f_new = (1/2 * 0.79 m) * sqrt((T + 3.2 N) / μ)
Since we don't have the exact value for linear mass density (μ), we are unable to calculate the new frequency accurately.
If you have additional information or the value of μ, we can proceed with the calculation. Otherwise, we need further specifics to provide a precise answer.