Stiffness is what you're looking for, according to the problem statement...Torrie said:Homework Statement
I have a mass of 100 g and I want to make it oscillate with a period of 10 Hz. What spring stiffness do I need?
Homework Equations
f = 1/2π√s/m
The Attempt at a Solution
I don't know how to find the stiffness to plug into the equation.
What have you tried? You have a relevant equation that contains the stiffness variable...Torrie said:Right, but I can't figure out how to find it!
First you'll need to convert the grams to kilograms. You need to use consistent units.Torrie said:Well I tried to isolate s, but I can't figure out how.
f = 1.57 x √s/100
10/1.57 = √s/100
6.369 x 100 = √s
636.94267^2 = s
405695.97 but I know this can't be right.
Because you are squaring both sides of the equation, so everything gets squared on both sides. More specifically, the right hand side of your equation has two main terms, ##\frac{1}{2\pi}## and ##\sqrt{\frac{s}{m}}##. Call them ##a## and ##b##. You should remember from algebra class that ##(a \cdot b)^2 = a^2 b^2## .Torrie said:Okay why would I square the 2π? Sorry I just want to make sure I am clear. Thank you so much for your help.
Looks good except for your value for the mass. As a result your answer is off by a power of ten. Check your conversion from 100 g to kg.f = 1/2π x √s/m
f^2 = 1/(2π)^2 x s/m
10^2 = 1/39.4384 x s/.01
100 = .025355 x s/.01
100 / .025355 = s/.01
3943.995 x .01 = s
39.43995 = s
Sound is a form of energy that is created by vibrations. These vibrations are transmitted through a medium, such as air or water, and travel in the form of waves.
Sound is produced when an object vibrates, causing changes in air pressure which then travel as sound waves. This vibration can be caused by various sources such as vocal cords, musical instruments, or even a car engine.
Frequency is the number of sound waves that pass a specific point in one second. The higher the frequency, the higher the pitch of the sound. This means that sounds with higher frequencies will have a higher pitch, while sounds with lower frequencies will have a lower pitch.
In the context of mass on a spring, the mass of an object affects the frequency of the sound wave it produces. A heavier mass on a spring will vibrate at a lower frequency, resulting in a lower pitch sound. Conversely, a lighter mass on a spring will vibrate at a higher frequency, creating a higher pitch sound.
The spring acts as a medium for the vibrations of the object, allowing the sound waves to travel through it. The properties of the spring, such as its tension and length, can also affect the frequency and amplitude of the sound produced by the vibrating object.