Tension is maintained in a string by attaching one end to a wall and by hanging a 2.34 kg object from the other end of the string after it passes over a pulley that is 2.00 m from the wall. The string has a mass per unit length of 3.45 mg/m. What is the fundamental frequency of this string?
Please help. do I use f=1/2L sqrt(tension/wavelenght)? Thank you.
The tension T = mg = 2.34•9.81 = 23 N.
m(o) = 3.45•10^-6 kg/m
v = sqrt(T/m(o)) =
=sqrt(23/(3.45•10^-6)) = 2582 m/s.
The fundamental frequency occurs when there is only one standing wave, or half a wavelength.
So, λ is equal by twice the 2 m length.
Thus, f = v/λ = v/2L = 2582/(2•2) = 645,5 Hz
I think,
Fundamental frequency,
f = v/lamda = v/(4L)
Because one end is node(fixed) and other is antinode (free to vibrat)
To find the fundamental frequency of the string, you can use the formula:
f = 1 / (2L) * sqrt(Tension / μ)
Where:
f is the frequency
L is the length of the string
Tension is the tension in the string
μ is the mass per unit length of the string
In this case, the length of the string (L) is 2.00 m and the mass per unit length (μ) is 3.45 mg/m.
To calculate the tension in the string, you need to consider the weight of the object hanging from the string. The weight of the object can be calculated using:
Weight = mass * gravity
Where:
mass is the mass of the object hanging from the string, which is 2.34 kg
gravity is the acceleration due to gravity, which is approximately 9.8 m/s^2
Weight = 2.34 kg * 9.8 m/s^2 = 22.932 N
Since the string is in equilibrium, the tension in the string is equal to the weight of the object.
Tension = 22.932 N
We can now substitute the values into the formula to find the fundamental frequency:
f = 1 / (2 * 2.00 m) * sqrt(22.932 N / (3.45 * 10^-3 kg/m))
Simplifying the equation:
f = 1 / 4.00 m * sqrt(22.932 N / (3.45 * 10^-3 kg/m))
f = 0.25 Hz
Therefore, the fundamental frequency of this string is 0.25 Hz.
To find the fundamental frequency of the string, you need to consider the tension in the string, the mass per unit length, and the length of the string.
First, let's calculate the tension in the string. The tension in the string can be determined using the weight of the object hanging from one end of the string. The weight of the object is given by:
Weight = mass × acceleration due to gravity
Weight = 2.34 kg × 9.8 m/s²
Weight = 22.932 N
Since the string passes over a pulley, the tension in the string on both sides of the pulley is equal. Therefore, the tension in the string is also 22.932 N.
Next, let's calculate the wavelength of the fundamental mode. The wavelength can be calculated using the formula:
wavelength = 2 × length
wavelength = 2 × 2.00 m
wavelength = 4.00 m
Now that we have the tension and wavelength, we can calculate the frequency using the formula:
frequency = sqrt(tension / (mass per unit length × wavelength))
mass per unit length = 3.45 mg/m = 3.45 × 10⁻⁶ kg/m
frequency = sqrt(22.932 N / (3.45 × 10⁻⁶ kg/m × 4.00 m))
Calculating the above expression will give you the value of the fundamental frequency of the string in Hz.