Amplitude of Wave at 5pi/6 Radians in Cycle, y = Asin(kx-wt)

[morrobay]

Homework Statement

λ = 3m
T = .5 s
k= 2π/λ = 2.09 radians/m
ω= 2π/T = 12.56 = radians/sec
v = ω/k = 6m/sec
At π radians with sin wave x = 3m
At 5π radians/6, x = 2.48 m
t = 2.48m/6m/sec = .41 sec
What is y at x,t
At t₀ x = t = 0
[/B]

Homework Equations

y = Asin(kx-ωt)[/B]

The Attempt at a Solution

y Asin (2.09)(2.48) - (12.56)(.41) = 5.18 - 5.14 = sin .04 = .0399 ?
From inspection of a unit circle/sine wave graph with y = A at 90⁰. π/2 radians = 1
.039 above is not correct
https://www.desmos.com/calculator/kxfekf0kgb[/B]

 

[haruspex]

"Amplitude of Wave at 5pi/6 Radians in Cycle"
What does this mean? "In cycle" suggests a point in time, but at what point in the x direction?
Please state the problem exactly as given to you.

 

[morrobay]

All data is in category 1 above : at t = .41 sec , v= 6m/sec x = 2.48 m also 150/180 (3m) = 2.48 m
The question: What is y ( amplitude of sine wave at 150⁰) , or 5pi/6 radians
A max = 1
www.desmos.com/calculator/cpb0oammx7

(clikck on 14 sine animation)

 

[haruspex]

All data is in category 1 above : at t = .41 sec , v= 6m/sec x = 2.48 m also 150/180 (3m) = 2.48 m
The question: What is y ( amplitude of sine wave at 150⁰) , or 5pi/6 radians
A max = 1

Then my best guess is that it means kx-ωt=5π/6, but then you do not need to know the wavelength or the period.

In your attempt in post #1 you calculated both an x and a t from one piece of information. This cannot be valid.

 

[morrobay]

Then my best guess is that it means kx-ωt=5π/6, but then you do not need to know the wavelength or the period.

In your attempt in post #1 you calculated both an x and a t from one piece of information. This cannot be valid.

Why ? I have v from ω/k above so at 2.48 m, t = .41 sec
y ( amplitude) = Asin(kx-ωt) for 5pi/6 ( x = 2.48) radians in the cycle see animation above.
I have shown x = 2.48 m twice above and t=.41 sec also and I repeated question in post # 2

 

[haruspex]

so at 2.48 m, t = .41 sec

The 2.48m you calculated as 5/6 of a wavelength. (Actually, you should have found 5/12 of a wavelength; 5π/6 radians is 5/12 of a cycle.)
So 0.41s is the time it takes to travel 5/6 of a wavelength.
You then found the amplitude at offset x at time t. If you think about it, that should have given you zero.
At (0,0) the amplitude is zero, and the wave moves in the positive x direction at speed v, so at (vt,t) it is also zero.

Let's do your calculation more accurately: x=2.5m (exactly)
kx-ωt=(2π/3)2.5-(2π/0.5)(2.5/6)=0.

The question can be made sensible in three ways (at least):

• specify an x position and ask for the amplitude at time 5T/12.
• specify a time and ask for the amplitude at 5λ/12.
• interpret it as asking or A sin(5(2π)/12).

 

[morrobay]

Then at x = 80m and t = 3.3 s. y = sin 125.9 = .81 And this is valid even when wave has not arrived at 80m ?"

 

[haruspex]

Then at x = 80m and t = 3.3 s. y = sin 125.9 = .81

Since the wavelength is 3m, what is happening at 80m is the same as is happenng at the same instant at 2m. Likewise, since the period is .5s, 3.3s is equivalent to 0.3s.
Since the speed is 6m/s, the wave at 2m after 0.3s is the same as the wave at 2-6x0.3 = 0.2m at time 0.
That is 0.2/3 of a wavelength, so (0.2/3)x2π radians or 24 degrees.

And this is valid even when wave has not arrived at 80m ?"

The wave equation gives you the amplitude at all times and all distances. It is infinite in length, so there is concept of its arrival.

 

[rude man]

Homework Statement

λ = 3m
T = .5 s
k= 2π/λ = 2.09 radians/m
ω= 2π/T = 12.56 = radians/sec
v = ω/k = 6m/sec
At π radians with sin wave x = 3m
At 5π radians/6, x = 2.48 m
t = 2.48m/6m/sec = .41 sec
What is y at x,t
At t₀ x = t = 0
[/B]

Homework Equations

y = Asin(kx-ωt)[/B]

The Attempt at a Solution

y Asin (2.09)(2.48) - (12.56)(.41) = 5.18 - 5.14 = sin .04 = .0399 ?
From inspection of a unit circle/sine wave graph with y = A at 90⁰. π/2 radians = 1
.039 above is not correct
https://www.desmos.com/calculator/kxfekf0kgb[/B]

As post#4 suggested, did you try Asin(kx-wt) with A=1 and kx-wt = 5pi/6?