Find the phase difference between these two sine waves

[hello478]

Homework Statement

At time t = 0 waves are in phase. At dotted line, t = 18 s.
At which time is phase difference between the two oscillations ⅛ of a cycle?
A 4.0 s B 4.5 s C 8.0 s D 9.0 s

Relevant Equations

answer is B

attempt:
4 waves in first wave
4.5 waves in second wave
0.5 is the difference
and so they are in anti-phase at 18 secs
180º = phase difference for 18 secs
so then after that i cant figure a way to solve it out...

 

[kuruman]

Homework Statement: At time t = 0 waves are in phase. At dotted line, t = 18 s.
At which time is phase difference between the two oscillations ⅛ of a cycle?
A 4.0 s B 4.5 s C 8.0 s D 9.0 s
Relevant Equations: answer is B

attempt:
4 waves in first wave
4.5 waves in second wave
0.5 is the difference
and so they are in anti-phase at 18 secs
180º = phase difference for 18 secs
so then after that i cant figure a way to solve it out...

What dotted line?

 

[hello478]

What dotted line?

sorry forgot to upload pic, edited it now

 

[nasu]

What is the phase difference, in cycles, at the dotted line?

 

[hello478]

What is the phase difference, in cycles, at the dotted line?

it is 180º, i wrote that in my attempt

 

[nasu]

Not in degrees, in cycles. You want to find when the phase difference is 1/8 of a cycle, not a specific angle.

 

[hello478]

Not n degrees, in cycles?

0.5 cycles or 0.5 wavelength...

 

[nasu]

Then it took 18 seconds to be out of phase by 1/2 cycle. How long for 1/8 cycles?

 

[hello478]

Then it took 18 seconds to be out of phase by 1/2 cycle. How long for 1/8 cycles?

so
18 : 0.5
x : 0.125
x= 4.5 s
omggg thats the answer thank you soooo much
but listen, how would we do it if i wanted to solve it in degrees? is that possible
and how would i know that i had to take cycles for this question? and can you please explain more about it

 

[nasu]

The question is when the phase difference is 1/8 cycle. It's a good practice to read the question carefully. What do you mean by "solve in degrees"? You could "convert" the cycles to degrees if you want but what's the point?

 

[hello478]

The question is when the phase difference is 1/8 cycle. It's a good practice to read the question carefully. What do you mean by "solve in degrees"? You could "convert" the cycles to degrees if you want but what's the point?

ok thanks alot
1 more question
isnt 1 cycle = 1 wave?
so wouldnt be the cycles for each wave be different
and we are using the ratio method here?
if i convert it to degrees
answer would be
18 = 180
x = 180/8
so x would be 2.25

 

[hello478]

The question is when the phase difference is 1/8 cycle. It's a good practice to read the question carefully. What do you mean by "solve in degrees"? You could "convert" the cycles to degrees if you want but what's the point?

please reply to my question when possible

 

[BvU]

Reconsider your conversion from cycles to degrees...

 

[hello478]

is it
0.5 : 180
0.125 : x
x= 22.5
and then
18 : 180
y : 22.5
y = 4.5 seconds
but 1 thing i dont understand is that
why is everything in cycles?
1 cycle means 1 wave right??
so is the phase difference in cycles or what?

 

[BvU]

A full cycle of a sine wave is up, down and up again:

$2\pi$ is a full cycle, 360 degrees.

[edit] the next paragraph belongs in the other thread (where 100 was't in the answers, but 260 was)

Things repeat after that. So there is no distinction between 100 degrees behind and 260 degrees ahead. Check it out with a few strips of paper with two or three cycles drawn on them

$\$

 

[hello478]

A full cycle of a sine wave is up, down and up again:
View attachment 341727

$2\pi$ is a full cycle, 360 degrees. Things repeat after that. So there is no distinction between 100 degrees behind and 260 degrees ahead. Check it out with a few strips of paper with two or three cycles drawn on them

$\$

so like...
if its supposed to be the same after 1 complete wave, then why is the phase difference different at 18 sec and 4.5 sec?
im sorry, im getting really confused
can you please explain cycles for this question in simple words without graphs...
tbh its making my mind go in cycles

 

[BvU]

so like...
if its supposed to be the same after 1 complete wave, then why is the phase difference different at 18 sec and 4.5 sec?

Now you are talking about TWO waves

I see I made a dreadful mistake mixing up your two threads. Sorry. Tried to edit a bit.

In the two waves case in this thread, the phase difference grows from 0 to $\pi$ in 18 sec. So it will be $2\pi$ after 36 sec. And the graph from time 36 to 54 sec will look exactly the same as that from t=0 to 18 sec.

$\$

 

[hello478]

i think i sort of get it
thank you soooo much

 

[hello478]

Now you are talking about TWO waves

I see I made a dreadful mistake mixing up your two threads. Sorry. Tried to edit a bit.

In the two waves case in this thread, the phase difference grows from 0 to $\pi$ in 18 sec. So it will be $2\pi$ after 36 sec. And the graph from time 36 to 54 sec will look exactly the same as that from t=0 to 18 sec.

$\$

so what is cycles???

 

[haruspex]

so what is cycles???

A cycle is the process of going from being in a certain state to next being in the same state. Imagine running around a circular track. Each lap is a cycle.
Assuming constant speed, 1/8 of a cycle can be thought of as 1/8 of the time to complete a lap or as going 1/8 of the way around. In a sine wave, the phase angle traversed in time t is $\omega t$, $\omega$ being constant, so 1/8 of a cycle can be thought of as an eighth of a period or a $2\pi/8$ advance in phase angle, it makes no difference.

 

[BvU]

i think i sort of get it
thank you soooo much

Don't worry, it will make sense after a while.

$\$

 

[hello478]

thank you