# Resonance frequency and Natural frequency?

Resonance frequency and Natural frequency??

Say there is an empty bottle of coke., and you know for sure that
the bottle resonates most at 320hz.
when the bottle resonates, the bottle will vibrate.
the question is,
1.if the bottle also resoates at 318hz( bu not most), will the bottle vibrate 318 times per second or 320times per second.?

2.What is the difference between resonance frequency and resonance frequency?? Aren't they basically the same??

haruspex
Homework Helper
Gold Member

Say there is an empty bottle of coke., and you know for sure that the bottle resonates most at 320hz.
when the bottle resonates, the bottle will vibrate.
the question is,
1.if the bottle also resonates at 318hz( but not most), will the bottle vibrate 318 times per second or 320times per second.?
As I read it from http://en.wikipedia.org/wiki/Harmonic_oscillator#Sinusoidal_driving_force, it will resonate at the driving frequency.
2.What is the difference between resonance frequency and resonance frequency?? Aren't they basically the same??
I assume that's not what you meant to ask.

Simon Bridge
Homework Helper

Welcome to PF;
A simple harmonic oscillator resonates at the natural frequency of the undamped form of the oscillator.

http://en.wikipedia.org/wiki/Harmonic_oscillator#Driven_harmonic_oscillators

However, the phenomenon of resonance is not restricted to simple harmonic oscillators.
http://en.wikipedia.org/wiki/Resonance

if you drive an oscillator - it will vibrate at the driving frequency.
if the driving frequency is not the resonant frequency, then the amplitude of the oscillations will be lower.
(See first link above "sinusoidal driving force".) The exact details depend on how the oscillator is driven.

Some systems will have more than one resonant frequency - i.e. a length of string can resonate in a series of modes though only the fundamental would be thought of as the "natural" frequency of the string.

Last edited:
Philip Wood
Gold Member

I don't find the term 'resonance frequency' very helpful. I prefer 'natural frequency'; it is the frequency of the body's free oscillations, so it is defined independently of forced oscillations. The phenomenon of resonance is that forced oscillations have maximum amplitude when the applied forcing frequency is at (or very near) the body's natural frequency. When the body has more than one natural frequency, I'd expect peaks of amplitude when the forcing frequency is equal to any of these frequencies.

Simon Bridge
Homework Helper

I don't find the term 'resonance frequency' very helpful
because you tend to confuse the phenomenon, "resonance" with the property "resonant"? I can see where thet would be a pain. Unfortunately,
the body's natural frequency
... has been goniffed by the pseudoscience, alt-medicine, crystal healing, etc. crowd. I live on an island retreat for such people so I cannot use that term without trouble ;)

Philip Wood
Gold Member

My unease about "resonance frequency" is that students who use the term know that this is the frequency of applied force at which a body's oscillations have maximum amplitude, but they don't always know that this frequency is that of the body's free (unforced) oscillations (or close to it).

sophiecentaur