Confused which equation to use - mechanical wave

[lumpyduster]

From EK 1001:

If the frequency of a simple harmonic, mechanical wave wave is doubled, its energy:

A. Decreases by factor of 2
B. Remains the same
C. Increases by factor of 2
D. Increases by a factor of 4

I thought C, the correct answer is D.

I used the equation E = hf.

EK used the equation I = 1/2*rho*w^2*A^2*v. Since w = 2pi*f, doubling the frequency quadruples the intensity of the wave, which is why D is correct. Honestly, I didn't come across this intensity equation in my reviewing, so maybe that's why I got it wrong. I do vaguely remember it from physics but anyway...

Why was I wrong to use E=hf?

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[Czarcasm]

From EK 1001:

If the frequency of a simple harmonic, mechanical wave wave is doubled, its energy:

A. Decreases by factor of 2
B. Remains the same
C. Increases by factor of 2
D. Increases by a factor of 4

I thought C, the correct answer is D.

I used the equation E = hf.

EK used the equation I = 1/2*rho*w^2*A^2*v. Since w = 2pi*f, doubling the frequency quadruples the intensity of the wave, which is why D is correct. Honestly, I didn't come across this intensity equation in my reviewing, so maybe that's why I got it wrong. I do vaguely remember it from physics but anyway...

Why was I wrong to use E=hf?

Sorry, I don't know what the heck I just wrote, so I deleted it. But basically, I think knowing frequency and amplitude squared are proportional to intensity can be very useful in some instances. As far as I've seen,, E=hf is applicable to light and it's wave-photon duality properties (a different energy). Probably best to just commit the variable relationships to memory - might prove helpful, but I'd be interested in hearing what someone with more experience has to say. Definitely not a fan of physics, so my knowledge is limited.

 

[lumpyduster]

Yeah I figure that it has something to do with it not being light! Physics is the hardest for me. After I got this question wrong I added that intensity equation to my list

 

[Czarcasm]

Yeah I figure that it has something to do with it not being light! Physics is the hardest for me. After I got this question wrong I added that intensity equation to my list

Yeah, physics isn't my strong point. But the good thing is, MCAT Physics is really oversimplified (some might argue otherwise, but it's true). It really could be worse. I think if you created a condensed sheet of equations and just started at them for a while, you'll probably realize it's not all that bad. I think the hard part is reading a question, finding an approach by extracting what you know and then just being able to get the info you need from a passage. I think this is really why scores vary so much between test takers imo.

Hang in there, it'll get easier.

 

[justadream]

@Czarcasm

"But basically, I think knowing frequency and amplitude squared are proportional to intensity can be very useful in some instances."

How does that show that frequency is proportional to energy-squared?

I guess you are implying that amplitude is directly proportional to energy? (I am unclear about this myself)?

 

[type12]

@Czarcasm is right: you need to know the effect velocity and amplitude have on intensity. Velocity is proportional: you double it, the intensity is doubled; amplitude is exponential: you double it, intensity goes up by four.

E = hf is the energy of a photon. It cannot be used for all waves, only for electromagnetic waves.

 

[justadream]

@type12

How do you know velocity doubles when frequency doubles?

 

[type12]

@type12

How do you know velocity doubles when frequency doubles?

Depending on the situation (like changing media), the frequency may or may not change. I didn't anything about the frequency, only the velocity.

 

[justadream]

@type12


I thought you were implying that velocity and frequency are directly related since the questions asks about a doubling of frequency.

So you are saying higher velocity and higher amplitude = higher intensity. But my question (and question of the OP) is how exactly you relate frequency with energy.

So how do you connect frequency with either velocity/amplitude/something else?

 

[justadream]

Actually now that I think about it, why does frequency even affect intensity?

I thought intensity (and energy) were proportional to Amplitude Squared. And amplitude is independent of velocity/frequency?

 

[type12]

I'm lost what the issue is: you have the equation there.

I = blah * blah * w^2 * blah * blah * v
w = 2*pi*f

I = blah blah * (2pi * f)^2

You are 100% correct that amplitude is not affected by frequency. Only intensity has a direct relationship with energy for mechanical waves.

 

[The Brown Knight]

I agree with Czarcasm on two points:
For MCAT purposes, know E=hf for light and that energy/power/intensity are proportional to amplitude squared AND frequency squared, though the passage would probably provide you with this.
The difference as was said probably has to do with the different kinds of energy being propagated - you can never represent mechanical waves simultaneously as minute particles like photons. Also, E = hf represents quanta of energy whereas mechanical waves propagate a continuum of energy.
Point is, some quantum calculations went into deriving E = hf and observation and Newtonian mechanics went into deriving the (more complicated) mechanical wave equation mentioned by OP (ironic, right?).

 

[justadream]

@The Brown Knight

So is the full statement of the equation:

Energy/power/intensity are proportional to amplitude squared AND frequency squared and wave velocity, and density*?

*Is "density" what "rho" is in the equation?

 

[The Brown Knight]

@The Brown Knight

So is the full statement of the equation:

Energy/power/intensity are proportional to amplitude squared AND frequency squared and wave velocity, and density*?

*Is "density" what "rho" is in the equation?

Yes.

 

[justadream]

Yes.

I looked up the equation in EK.

Why do they use "ANGULAR frequency" instead of just frequency?

 

[type12]

I looked up the equation in EK.

Why do they use "ANGULAR frequency" instead of just frequency?

Have to, waves are sinusoidal:

http://en.wikipedia.org/wiki/Sine_wave

Think radians (but not for MCAT, MCAT don't care for radians).

 

[justadream]

Have to, waves are sinusoidal:

http://en.wikipedia.org/wiki/Sine_wave

Think radians (but not for MCAT, MCAT don't care for radians).

Don't you use radians when discussing angular velocity/acceleration (MCAT topics)?

 

[type12]

Don't you use radians when discussing angular velocity/acceleration (MCAT topics)?

Angular velocity and angular acceleration are not on the MCAT.

 

[justadream]

Angular velocity and angular acceleration are not on the MCAT.

Lol really? I was always unclear about that since review books tend to cover it a little bit.

If those aren't covered, doesn't that imply that angular momentum stuff isn't covered as well?

 

[type12]

Lol really? I was always unclear about that since review books tend to cover it a little bit.

If those aren't covered, doesn't that imply that angular momentum stuff isn't covered as well?

There are topics that need angular velocity and acceleration to be explained/understood. I can't talk about what ice is unless we also talk about water.

 

[The Brown Knight]

I looked up the equation in EK.

Why do they use "ANGULAR frequency" instead of just frequency?

You can use EITHER by substituting with the relationship: w = 2(pi)f (w = angular frequency and f = regular frequency)
in other words, frequency is oscillations per second while angular frequency is radians per second because of unit conversion:
w radians per second = (2pi radians/oscillation) (f oscillations per second)
angular frequency is LITERALLY that: the angular version of frequency (just as angular acceleration is angular version of acceleration, torque is angular version of force, etc.)