Mechanical wave...

[BestDoctorEver]

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If the speed of a simple harmonic, mecahnical wave is doubled, its energy:

A. decreases by a factor of 2.
B. remains the same.
C. increases by a factor of 2.
D. increases by a factor of 4.

They say that the answer is C. I believe it should be D. What am I missing here?

This problem is on EK 1001 Physics...I think they make a mistake in the answer key.

 

[BestDoctorEver]

If the speed of a simple harmonic, mecahnical wave is doubled, its energy:

A. decreases by a factor of 2.
B. remains the same.
C. increases by a factor of 2.
D. increases by a factor of 4.

They say that the answer is C. I believe it should be D. What am I missing here?

This problem is on EK 1001 Physics...I think they make a mistake in the answer key.

Bump...

 

[gunj122]

not sure but...
v = (wavelength)(freq) --> freq = (2v)/(wavelength)

E = (planks constant)(freq) --> 2E = (planks constant)(2v)/(wavelength)

 

[flodhi1]

Bump...

Dude
1) Energy = hf

Since
2) frequency = velocity / wavelength
Plugging equation 2 into equation 1

Energy = h * v / wave length

Thus I would assume since Velocity doubles so should the energy since they are directly proportional with no power difference.

Therefore Answer C is correct

What you are stating is that Energy = h x v^2 / wave length

Which is obviously NOT true. Thus your answer D is incorrect.

 

[Cosmic]

Dude
1) Energy = hf

Since
2) frequency = velocity / wavelength
Plugging equation 2 into equation 1

Energy = h * v / wave length

Thus I would assume since Velocity doubles so should the energy since they are directly proportional with no power difference.

Therefore Answer C is correct

What you are stating is that Energy = h x v^2 / wave length

Which is obviously NOT true. Thus your answer D is incorrect.

First of all, isn't E=hf the energy of a photon. What does that have to do with the energy of a wave?

Secondly, couldn't the velocity have doubled by doubling the wavelength? In this case, the energy would be decreased by a factor two (assuming it's okay to even use this equation to begin with).

Third, to OP - what number is this question in EK 1001 because I don't see it listed anywhere within the wave section.

 

[flodhi1]

First of all, isn't E=hf the energy of a photon. What does that have to do with the energy of a wave?

Secondly, couldn't the velocity have doubled by doubling the wavelength? In this case, the energy would be decreased by a factor two (assuming it's okay to even use this equation to begin with).

Third, to OP - what number is this question in EK 1001 because I don't see it listed anywhere within the wave section.

Yeah posted the wrong equation

 

[ilovemcat]

I'm not sure why you guys are assuming frequency doubled since the frequency of a wave itself is dictated by the source it originates from. The question mentions nothing about a change in frequency. Either way, a change in frequency wouldn't change the speed of the wave, because the speed of the wave is dictated by the medium it's traveling through. In fact, doubling the frequency would require the wavelength decrease proportionally in order to maintain a constant velocity. However, this question mentions there WAS a change in velocity (chances are, the medium changed as well). Because the velocity doubled and frequency is dictated by the source (ie. remains constant), wavelength must double. However, the wavelength is irrelevant to this question. The energy for a mechanical wave is proportional to the intensity of the wave, which in turn is proportional to velocity. Therefore, if the velocity doubles, intensity will double. Finally, if the intensity doubles, energy will double. By the way, as Cosmic mentioned, the energy equation you guys are also using is the energy of a photon (an electromagnetic wave); it does not apply here.

 

[gunj122]

I'm not sure why you guys are assuming frequency doubled since the frequency of a wave itself is dictated by the source it originates from. The question mentions nothing about a change in frequency. Either way, a change in frequency wouldn't change the speed of the wave, because the speed of the wave is dictated by the medium it's traveling through. In fact, doubling the frequency would require the wavelength decrease proportionally in order to maintain a constant velocity. However, this question mentions there WAS a change in velocity (chances are, the medium changed as well). Because the velocity doubled and frequency is dictated by the source (ie. remains constant), wavelength must double. However, the wavelength is irrelevant to this question. The energy for a mechanical wave is proportional to the intensity of the wave, which in turn is proportional to velocity. Therefore, if the velocity doubles, intensity will double. Finally, if the intensity doubles, energy will double. By the way, as Cosmic mentioned, the energy equation you guys are also using is the energy of a photon (an electromagnetic wave); it does not apply here.

so what equation relates intensity and energy? how do we know if its a y=x^2 or y=x relationship?

 

[BestDoctorEver]

First of all, isn't E=hf the energy of a photon. What does that have to do with the energy of a wave?

Secondly, couldn't the velocity have doubled by doubling the wavelength? In this case, the energy would be decreased by a factor two (assuming it's okay to even use this equation to begin with).

Third, to OP - what number is this question in EK 1001 because I don't see it listed anywhere within the wave section.

It's number 929 in Optics

 

[plzNOCarribbean]

with harmonics,

f= n v/2L

so, because the velocity doubles, the frequency should also double. Now, this equation applies to harmonic frequencies, so I am not sure why we would use the equation E=hf, because that applies to electromagnetic waves, which are not mechanical waves.

electromagnetic waves do not require a medium through which to travel, whereas all mechanical waves require some medium to propagate through. Thats why, I could see why doubling frequency would correlate with a doubling of the energy, but not in this case because the equation E=fh applies only to electromagnetic radiation.

 

[Sonyfan08]

Wouldn't the energy be the same since the energy of the simple harmonic wave is directly proportional to amplitude and independent of frequency/period?

 

[vayntraubinator]

A wave transfers energy and momentum.

My thought process was, if velocity doubled, then according to p=mv, momentum doubled.

Must have double the energy since they're directly proportional. C

 

[plzNOCarribbean]

A wave transfers energy and momentum.

My thought process was, if velocity doubled, then according to p=mv, momentum doubled.

Must have double the energy since they're directly proportional. C

^correct me if im wrong but I don't think you can do this. Just because momentum doubled, it doesn't mean energy doubles. there is no equation relating momentum to energy.

 

[Majik]

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[inaccensa]

I know this equation is found sound, but i was thinking since it is a mechanical wave, cant we use,Intensity = 1/2Amplitude^2(omega)^2*density*velocity
In short I is directly proportional to velocity
Intensity = Power /Area
=(Energy/time)/area

If Intensity doubles, Energy will double which will happen when velocity doubles