A couple of questions on waves

[sv3]

So I went over the first section of waves in TPR (still have sound and optics to do) and wanted to see if I could clear a few things up before continuing with your help of course:

1) For a pendulum, TPR first says the restoring force is gravity and F=mgsinQ. Two lines later it says a pendulum isn't technically an example of SHM since mgsinQ isn't proportional to Q. They state that if Q is small enough, you can use F= mgQ since mgQ is proportional to Q. Can anyone clarify this? Which one should I be using as the restoring force for a pendulum?

2) For the equation speed = root of tension/linear density: is this only good for transverse waves on a rope? Or can you apply it in other scenarios? (and btw, why speed and not velocity for all this wave business.....I'm sure I'll kick myself after hearing the answer)

3) This is one that bugs me alot. If you have a wavelength that fits the condition for a standing wave, can you just use that harmonic number to find the corresponding frequency? Or can you not relate the two harmonic numbers? (perhaps you need to be given speed and work backwards). I'm just confused as to whether or not the harmonic numbers for wavelength and speed are related.....or if their equations just look similar. I'm thinking perhaps the MCAT will say here are frequencies and wavelength pairs, which pair satisfies the conditions for a standing wave and I'm seeing if there's an effecient way of tackling this type of hypothetical.

many thanks

PS (yes i know i said a couple of questions.....my bad)

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[Fort]

So I went over the first section of waves in TPR (still have sound and optics to do) and wanted to see if I could clear a few things up before continuing with your help of course:

1) For a pendulum, TPR first says the restoring force is gravity and F=mgsinQ. Two lines later it says a pendulum isn't technically an example of SHM since mgsinQ isn't proportional to Q. They state that if Q is small enough, you can use F= mgQ since mgQ is proportional to Q. Can anyone clarify this? Which one should I be using as the restoring force for a pendulum?

2) For the equation speed = root of tension/linear density: is this only good for transverse waves on a rope? Or can you apply it in other scenarios? (and btw, why speed and not velocity for all this wave business.....I'm sure I'll kick myself after hearing the answer)

3) This is one that bugs me alot. If you have a wavelength that fits the condition for a standing wave, can you just use that harmonic number to find the corresponding frequency? Or can you not relate the two harmonic numbers? (perhaps you need to be given speed and work backwards). I'm just confused as to whether or not the harmonic numbers for wavelength and speed are related.....or if their equations just look similar. I'm thinking perhaps the MCAT will say here are frequencies and wavelength pairs, which pair satisfies the conditions for a standing wave and I'm seeing if there's an effecient way of tackling this type of hypothetical.

many thanks

PS (yes i know i said a couple of questions.....my bad)

1) They are using something called the small angle condition. Basically if the angle is less than 10 degrees, then we can say that sinQ = tanQ = Q, where Q is in radians. Personally, I would just stick to mgsinQ because I probably would't think to use the small angle condition on a pendulum problem, but it's your call. You won't be wrong for always using mgsinQ, but you will be wrong to use mgQ if Q ~> 10 degrees.

2) As far as I know, if it has tension, then you can use that equation whenever applicaple; wires are a very common application, not just ropes. It can also be used for standing waves like those on a piano or guitar.

Some books like to be consistent with their vector/scalar idealsims. Try not to get too hung up on this for the equation you're using because my text uses velocity, but I know they're talking about a scalar (speed) because velocity isn't bolded. Knowing the speed of the traveling wave is enough for the scope of the MCAT.

3) Yes, you can, it's quite simple for standing waves.

In general we can write

f = v/lambda where n is the harmonic number.

It seems strange, but you use the same speed when calculating harmonic properties for standing waves. The MCAT may give you the tension in the cord, or the speed to start with and ask you to make a judgment call on a wavelength/frequency pair.

 

[sv3]

1) They are using something called the small angle condition. Basically if the angle is less than 10 degrees, then we can say that sinQ = tanQ = Q, where Q is in radians. Personally, I would just stick to mgsinQ because I probably would't think to use the small angle condition on a pendulum problem, but it's your call. You won't be wrong for always using mgsinQ, but you will be wrong to use mgQ if Q ~> 10 degrees.

2) As far as I know, if it has tension, then you can use that equation whenever applicaple; wires are a very common application, not just ropes. It can also be used for standing waves like those on a piano or guitar.

Some books like to be consistent with their vector/scalar idealsims. Try not to get too hung up on this for the equation you're using because my text uses velocity, but I know they're talking about a scalar (speed) because velocity isn't bolded. Knowing the speed of the traveling wave is enough for the scope of the MCAT.

3) Yes, you can, it's quite simple for standing waves.

In general we can write

f = v/lambda where n is the harmonic number.

It seems strange, but you use the same speed when calculating harmonic properties for standing waves. The MCAT may give you the tension in the cord, or the speed to start with and ask you to make a judgment call on a wavelength/frequency pair.

Hi Fort,
Thanks a ton. Your response pretty much clarified things for me.

steve