"You will measure the tension T, the mass m, and the length L of your spring.
In terms of these variables, what is the expected frequency of the fundamental standing wave?"
I found the fundamental frequency to be:
f = 1/2L * sqrt(T/m/L)?
If you reconstruct the equation, you will get 1/2*(T/mL)^1/2
Well, well, well, someone's getting all technical with springs! So, you're looking for the expected frequency of the fundamental standing wave, huh? Let's see if I can break it down for you.
Now, according to my hilariously reliable sources, the formula you provided seems to be correct. It's all about that math magic. We have f = (1/2L) * √(T/m/L), where T is the tension, m is the mass, and L is the length of the spring.
In simpler terms, you're basically saying that the frequency, f, is proportional to the square root of the tension and inversely proportional to both the mass and the square root of the length. Ah, physics, you're such a joker!
So, next time you're dealing with springs and frequencies, just remember this equation and whip it out like a circus performer cracking a whip. Fingers crossed that you don't get tangled up in all those variables and equations. Happy springing!
Yes, that is correct. The formula you provided,
f = (1/2L) * sqrt(T/mL),
represents the expected frequency of the fundamental standing wave in terms of the variables tension (T), mass (m), and length (L) of the spring.
To calculate the fundamental frequency, you can use this formula by substituting the values of T, m, and L into the equation.
To find the expected frequency of the fundamental standing wave in a spring, you will need to use the given variables: tension T, mass m, and length L. The equation you mentioned is close, but there is a minor mistake in it.
The correct equation to find the expected frequency (f) of the fundamental standing wave in a spring is given by:
f = 1 / (2L) * sqrt(T / m)
Let's break it down step by step:
1. First, find the square root of the tension (T) divided by the product of mass (m) and length (L):
√(T / (m * L))
2. Next, divide 1 by 2L, which is the two times the length of the spring:
1 / (2L)
3. Finally, multiply these two results together:
f = 1 / (2L) * √(T / (m * L))
Now you have the correct equation to find the expected frequency of the fundamental standing wave in the spring, given the variables T, m, and L.