Physics question - phase difference

[Leeum]

Hi,

Having a little difficulty in doing this question:

A wave of frequency 5 Hz travels at 8 kms–1 through a medium. What is the phase difference, in radians, between two points 2 km apart?

A 0
B Pi/2
C Pi
D 3Pi/2

I understand the phase difference is (2Pi/Wavelength) x (X1-X2). This leaves me with the answer 7.85 which I assume is an angle - degrees? How do I convert that to Radians/ relate it to Pi.

Cheers

 

[Jonnycoupe]

180 degress/Pi = 1 radian.

therefore
1 radian = 57.296 degrees

Based on what value you have given and not redoing the working I'd go with 0.137 rads.

 

[misterPK]

You can understand phase difference and yet don't know what radians are?

The answer is in radians already. 7.85 = 3Pi/2

FOR FUTURE REFERENCE:
On my scientific calculator there's a radian-degrees converter button. You'll also find that there's a radian mode, so any calculations involving trig functions will be done in radians instead of degrees.

PK!

 

[Leeum]

I understand radians but I cant get my head around that question. The answer is supposedly B.

 

[SpeedFreak]

They are out of phase by 90 degrees which = pi/2 rads

v=f lamba
8=5 lamba
lamba= 1.6km

2km = 1.25 lamba

difference =0.25 lambda = 90 degrees.

draw a Sin wave and it will make sense

 

[misterPK]

It is B, you've just fallen into that questions evil trap. The formula will give you the answer of 3Pi/2, however you need to realise that once a wave has gone through a phase change of 2Pi, its back where it started again.

The way to remember it is that 2Pi is 360 degrees, so anything over that and you're going round the circle more than once. 3Pi/2 radians is 450 degrees, which is obviously the same as 90 degrees, which is Pi/2 radians.

Like I said its a sneaky evil trap to see if you can get your head round radians.

PK!

 

[Jonny69]

You can understand phase difference and yet don't know what radians are?

Steady on old chap, I really struggled with Radians at first

 

[Amleto]

The answer is in radians already. 7.85 = 3Pi/2

PK!

oh really?


hmm, 3 * pi / 2 is more like 4.71.



the asnwer from formula is 7.85. now take away as many integer multiples of two pi as you can - you get left with 1.5707...


ie pi/2, answer B

 

[misterPK]

Steady on old chap, I really struggled with Radians at first

Yeah, as you can see I didn't spot the mistake at first either! Sorry!

PK!

 

[misterPK]

oh really?


<Snip>

Oh dear god my ms calculator skills and lack of common sense really do suck. I'm really sorry for the lecture.

I will get off my high horse now and crawl in the mud where I belong. You can tell its been years since I did this stuff....

PK!

 

[Energize]

You can understand phase difference and yet don't know what radians are?

Exam boards teach phase differences before radians.