Spring Amplitude and Frequency

[MedPR]

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If the amplitude of the oscillatory motion is increased, the frequency of oscillation will:

A. increase
B. remain unchanged
C. decrease
D. depend upon the weight attached

The book doesn't have an answer, but I'm pretty sure it's C.

If you increase the amplitude, the period increases, thus decreasing the frequency by f = 1/T.

Also, can someone explain how f=1/T works? I understand that frequency is the number of complete cycles per unit of time, and the period is the time it takes to complete one cycle. For some reason I just can't get an intuitive understanding of the equation.

 

[Ssina]

why not B! isn't amplitude just the displacement from the rest, and freq how many cycles per second, so I don't see how having higher amplitude would affect the frequency. e.g. for spring the frequency is 1/2pi.sqrtk/m... so doubt amplitude would do anything to it?!

plus I just know T and f from what you just said, if T is high (meaning takes longer to complete a cycle) then freq is low (meaning it'll have less # cycles per second)

 

[MedPR]

why not B! isn't amplitude just the displacement from the rest, and freq how many cycles per second, so I don't see how having higher amplitude would affect the frequency. e.g. for spring the frequency is 1/2pi.sqrtk/m... so doubt amplitude would do anything to it

Wouldn't it take longer to do one 50m cycle than one 10m cycle?

 

[Ssina]

this is what I imagine from the question

so higher amplitude higher energy being transfered by the wave, but it didn't change the wavelength or the frequency of the wave... still have the same wavelength
EDIT: should add speed doesn't change either from v=lamda.f

 

[SaintJude]

why not B! isn't amplitude just the displacement from the rest, and freq how many cycles per second, so I don't see how having higher amplitude would affect the frequency. e.g. for spring the frequency is 1/2pi.sqrtk/m... so doubt amplitude would do anything to it?!

plus I just know T and f from what you just said, if T is high (meaning takes longer to complete a cycle) then freq is low (meaning it'll have less # cycles per second)

Yeah, I agree. I think it's B. I thought that frequency measures the rate at which the cycle is completed, regardless of circle size. As far as I understood, there are only two factors that affect frequency. In springs, it is the spring constant and mass. And in pendulum it is gravity and the length of the string.
But I also haven't gotten an intuitive understanding of this topic...could someone fill us in?

 

[milski]

Wouldn't it take longer to do one 50m cycle than one 10m cycle?

Frequency/period depends only on the stiffness of the spring and the mass of the body. You can have larger amplitude just by pushing on the spring with more force - that will give you the same frequency but larger amplitude. The larger cycle completes in the same amount of time because the velocities are larger.

 

[milski]

this is what I imagine from the question

so higher amplitude higher energy being transfered by the wave, but it didn't change the wavelength or the frequency of the wave... still have the same wavelength
EDIT: should add speed doesn't change either from v=lamda.f

Speed of the wave itself does not change. The max velocity (which is when crossing the neutral point) does increase when the amplitude increases.

 

[SaintJude]

Speed of the wave itself does not change. The max velocity (which is when crossing the neutral point) does increase when the amplitude increases.

Yeah, so it's B. But since we're at it... how do you know the maximum velocity increases?

 

[Ssina]

also velocity is a function of the tension and some constant density I think, from AO if I remember correctly, been a while since I've listen to them!

but it's like a audio amplifier, take energy from the electricity to increase the amplitude and make the sound louder but doesn't change the pitch/frequency of the sound

 

[MedPR]

Thanks, that makes sense now.

 

[milski]

Yeah, so it's B. But since we're at it... how do you know the maximum velocity increases?

The formulas are derived by solving a differential equation which come from the formula for the force and displacement of the spring. But even if you decide not to go in the math:
- if the frequency stays the same and the amplitude increase, the velocity has to increase - you're covering more distance in the same time.
- you can also consider it from energy point of view - when crossing the neutral point you have only kinetic energy, when at the most distant points - only potential. So you're completely converting from potential to kinetic and back. Since larger amplitude corresponds to larger displacement and more potential energy, you will end up with more kinetic energy at the neutral point and thus with higher speed.

 

[Ssina]

ok now I'm confused.... about sound waves only (not transverse), isn't amplitude/displacement for the longitudinal waves in the direction of wave propagation... then giving it more energy (intensity) they will be displaced faster... then it should affect the freq/wavelength.. right!?

 

[milski]

ok now I'm confused.... about sound waves only (not transverse), isn't amplitude/displacement for the longitudinal waves in the direction of wave propagation... then giving it more energy (intensity) they will be displaced faster... then it should affect the freq/wavelength.. right!?

For sound waves the source determines both the frequency and the amplitude. In that sense, you change either independently from the other.

 

[labradoodle]

Looks like you're working with TBR.

On the review page for that chapter it is stated that period and amplitude are independent from one another.

Frequency is simply 1/period. Frequency is therefore also independent from the amplitude.

 

[chiddler]

Looks like you're working with TBR.

On the review page for that chapter it is stated that period and amplitude are independent from one another.

Frequency is simply 1/period. Frequency is therefore also independent from the amplitude.

dude. this thread is older than my grandma.

 

[milski]

dude. this thread is older than my grandma.

But it was in desperate need of resolution. 😀

 

[487806]

Looks like you're working with TBR.

On the review page for that chapter it is stated that period and amplitude are independent from one another.

Frequency is simply 1/period. Frequency is therefore also independent from the amplitude.

FYI, OP's done with the MCAT long time ago, so your 10-month delayed response won't help. Next time, please don't revive old threads just to join in the conversation.

 

[MedPR]

FYI, OP's done with the MCAT long time ago, so your 10-month delayed response won't help. Next time, please don't revive old threads just to join in the conversation.

Yes and I'm very happy to be done. I can't answer any physics questions now.