Intensity, frequency and amplitude

[PFuser1232]

Homework Statement

A wave has an amplitude a₁, intensity I, and frequency f. A second wave of the same type has twice the intensity and double the frequency, find the amplitude of the second wave in terms of a₁.

Homework Equations

Using the relationship I=k a²f², where k is a constant:

The Attempt at a Solution

[itex]\frac{I}{a₁²f²}[/itex] = [itex]\frac{2I}{a₂²(0.5f)²}[/itex]
So a₂ = √8 a₁


But according to my answer key, the answer is √2 a₁

 

[BvU]

Homework Statement

A wave has an amplitude a₁, intensity I, and frequency f. A second wave of the same type has twice the intensity and double the frequency, find the amplitude of the second wave in terms of a₁.

Homework Equations

Using the relationship I=k a²f², where k is a constant:

The Attempt at a Solution

$\frac{I}{a_1^2 f^2} = \frac{2I}{a_2^2 ( 0.5 f )^2}$

So a₂ = √8 a₁


But according to my answer key, the answer is √2 a₁

Well, what did you do with "double the frequency" ?


TeX tips: within $[$ itex $]$ ... $[$ /itex $]$ a subscript is done using _ and a superscript is done using ^
so $[$ itex $]$ a^2_\epsilon $[$ /itex $]$ gives $a^2_\epsilon$

 

[PFuser1232]

I'm so sorry! I meant the frequency is halved.

 

[PFuser1232]

Well, what did you do with "double the frequency" ?


TeX tips: within $[$ itex $]$ ... $[$ /itex $]$ a subscript is done using _ and a superscript is done using ^
so $[$ itex $]$ a^2_\epsilon $[$ /itex $]$ gives $a^2_\epsilon$

I meant to say that the frequency is halved, can you look into it again?

 

[BvU]

Well, if the intensity isn't also halved, I agree with your a2 = √8 a1. Can't find a way to dismiss the relationship you're using. So, I'm puzzled.

 

[PFuser1232]

Well, if the intensity isn't also halved, I agree with your a2 = √8 a1. Can't find a way to dismiss the relationship you're using. So, I'm puzzled.

What I mean to say is, is the relationship between I a and f valid? Or is intensity just proportional to the square of the amplitude?

 

[BvU]

The latter could be quite right. I've seen it come by while googling around. But your orginal formula as well. Is there something in the context that can help you on your way (except for the answer that indeed points to I $\propto$ amplitude²) ? What is the subject of the chapter at hand ?

 

[PFuser1232]

The latter could be quite right. I've seen it come by while googling around. But your orginal formula as well. Is there something in the context that can help you on your way (except for the answer that indeed points to I $\propto$ amplitude²) ? What is the subject of the chapter at hand ?

It is on the basic properties of waves in general, and the question did not specify the type of wave.

 

[BvU]

Well, then the caveat is we've done it for e.g. electromagnetic waves. Sound or springs have I $\propto \omega^2$ amplitude² as you wrote.

Anyone else have an idea here ? I'm at a loss.