Yet another trig (sine wave) question

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Homework Help Overview

The discussion revolves around modeling a sine wave to represent the height of water waves during a storm, with specific parameters given such as the wave period and the height difference between the crest and trough.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the correct form of the sine wave equation, questioning whether a vertical shift is necessary to accommodate the trough at 0m. They discuss the implications of amplitude and phase shifts on the wave's representation.

Discussion Status

Participants are actively engaging with the problem, considering different interpretations of the sine wave equation and its parameters. There is a recognition of the ambiguity in the problem statement regarding the trough's position and how it affects the equation. Some guidance has been offered regarding the need for clarity on vertical versus horizontal shifts.

Contextual Notes

There is uncertainty about the interpretation of the variable used (x as time versus distance) and how it affects the wave's behavior. The problem does not explicitly state the phase of the wave at t = 0, leading to varied interpretations among participants.

Imperil
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During a storm, waves pass a fixed point every 2s. The difference between the crest and the trough of any wave is 5.2m

a) Write the equation of the sine wave that models the height of a point on the water wave.
b) Graph using 0m as the trough

My Answer:

2Pi / k = 2
k = Pi

2.6sinPi(x)

I wanted to check if this is correct?

I just wanted to make sure I was not supposed to shift vertically 2.6m?
i.e. 2.6sinPi(x) + 2.6

Originally I vertically shifted it 2.6 but then I couldn't figure the reason I did this (other than not going negative m). Then when I noticed part b said the trough is 0m I corrected my equation not to include the shift.
 
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Imperil said:
2.6sinPi(x)
…
I just wanted to make sure I was not supposed to shift vertically 2.6m?
i.e. 2.6sinPi(x) + 2.6

Originally I vertically shifted it 2.6 but then I couldn't figure the reason I did this (other than not going negative m). Then when I noticed part b said the trough is 0m I corrected my equation not to include the shift.

Hi Imperil! :smile:

(have a pi: π :wink:)

No, I'm pretty sure they never want you shift vertically,

but you may have to shift horizontally …

2.6sin(πx) is not a trough at x = 0, it's only "half-way up". :wink:
 
Ah so you are saying that my original thought of: 2.6sinPi(x) + 2.6

Is correct then because I need the center to be lifted by 2.6m in order to make the trough 0. Am I right in thinking this?
 
Imperil said:
Ah so you are saying that my original thought of: 2.6sinPi(x) + 2.6

Is correct then because I need the center to be lifted by 2.6m in order to make the trough 0. Am I right in thinking this?

Nope :redface: …

you've added 2.6 to y, so you've shifted the graph vertically …

you need to add something to x, to shift it horizontally :wink:
 
tiny-tim said:
Nope :redface: …

you've added 2.6 to y, so you've shifted the graph vertically …

you need to add something to x, to shift it horizontally :wink:
Ok I am a little confused

So for part A of the question my function 2.6sinPi(x) is correct because all it states is a sine wave with an amplitude of 2.6?

For part B I'm unsure why I need to phase shift because no matter how much I shift, the trough will always be -2.6 will it not? That is why I used a vertical translation of +2.6 which than gives a range of 0 <= y <= 5.2 ... whereas a phase shift will leave me with a range of -2.6 <= y <= 2.6 so I'm not sure how that will work?
 
Imperil said:
Ok I am a little confused

So for part A of the question my function 2.6sinPi(x) is correct because all it states is a sine wave with an amplitude of 2.6?

For part B I'm unsure why I need to phase shift because no matter how much I shift, the trough will always be -2.6 will it not? That is why I used a vertical translation of +2.6 which than gives a range of 0 <= y <= 5.2 ... whereas a phase shift will leave me with a range of -2.6 <= y <= 2.6 so I'm not sure how that will work?

Hi Imperil! :smile:

(just got up :zzz:)

I wonder whether we're talking about the same sort of graph?

I assumed since you're using x and y that they're both distances …

But if you're using x as time (I would have used t), then I agree it means y = 0m is the minimum (the trough), and your vertical translation is correct …

though then the value of t at which y = 0 is not specified. :confused:
 
Yes I am using X as time and Y as the height of the wave :)

Also that would leave the value of t at which y = 0 1.5s would it not?
2.6sin(Pi * 1.5) + 2.6 = 0

The big problem I have now though is part A of the question. Since it doesn't state to use 0m as the trough I believe the proper function is 2.6sinPi(x) without the vertical translation... but I'm not 100% sure if that is what they want and I have to hand this in today.
 
Imperil said:
The big problem I have now though is part A of the question. Since it doesn't state to use 0m as the trough I believe the proper function is 2.6sinPi(x) without the vertical translation... but I'm not 100% sure if that is what they want and I have to hand this in today.

ok … so x is time …

hmm … let's look at the question again …
Imperil said:
During a storm, waves pass a fixed point every 2s. The difference between the crest and the trough of any wave is 5.2m

a) Write the equation of the sine wave that models the height of a point on the water wave.
b) Graph using 0m as the trough

I think a) is asking for the equation for a fixed point on the surface of the water as it goes up and down (with no sideways movement).

neither a) nor b) tells you which part of the cycle the wave is at at t = 0, so you could chose any "phase factor", so you may as well choose 0.

Like you, I'm surprised that "using 0m as the trough" isn't in a) as well as b) (btw, it doesn't say "0s" does it?), but I think you'd better answer as if it is.
Also that would leave the value of t at which y = 0 1.5s would it not?
2.6sin(Pi * 1.5) + 2.6 = 0

sorry, where does 1.5 come from (and what happened to t or x)? :confused:
 
tiny-tim said:
ok … so x is time …
sorry, where does 1.5 come from (and what happened to t or x)? :confused:
Sorry the equation I listed t = 1.5s which then makes y = 0m
 

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