Waves - AS Physics

The picture attached is a picture of a rope with a stationary wave on it.

The point Y and Z apparently have no phase difference, but I don't see how this is? Surely it will be 45 degrees?

Any help would be great! Many thanks

phase.jpg39.1KB

Reply 1

uberteknik

Original post by tjthedj

The question tells you it's a stationary wave. By definition the points Y and Z are not travelling and therefore will stay in the same place.

Hence there can be no phase difference only displacement.

(edited 9 years ago)

Reply 2

username1673791

Original post by uberteknik

But the mark scheme also says that the phase difference between W and Y is 180 degrees? so not sure how it makes sense... i originally thought its 45 degrees out

not sure if the mark scheme is wrong?

Reply 3

Phichi

Original post by uberteknik

Original post by tjthedj

The points W and Y are moving, its a standing wave, they will just oscillate. They happen to be oscillating completely out of phase however. If you wanted to just analyse the phase, they are half a wavelength apart, hence 180 degrees, or

\pi

Y and Z are in phase, they both lie between the same nodes.

(edited 9 years ago)

Reply 4

uberteknik

Original post by tjthedj

Think about the motion of the points on the wave. They only move up and down so there can only be two values of phase for a standing wave:

pi = 180^o out of phase and

0⁰ = in phase.

There are no other instances.

Reply 5

A84

another question

can someone conform these equations?
what r they bout??

DSC01832.jpg326.9KB

Reply 6

Phichi

Original post by A84

another question

can someone conform these equations?
what r they bout??

What exactly don't you understand?

Reply 7

A84

Original post by Phichi

What exactly don't you understand?

Sorry, guess I could be more clearer.
In these equations, shouldn’t the length L be represented bysmall letter l?
And this is about Harmonics, what I don’t get is that arethese fixed equations to determining such harmonics or are they derived fromsomething else?
How can we tell in the exam, which harmonic is given in apicture?

Reply 8

Phichi

Original post by A84

The length doesn't have to be represented by l or L, it's just what was picked for convenience, L is probably the most suitable here. They aren't really equations as such, just intuition. You look at the picture, determine how many wavelengths it contains, and link that to the length. In the first harmonic, the picture shows one half of one wave cycle, hence half a wavelength, the total length is thus just half of the wavelength. The frequency of the harmonics is just general. If you have the 10th harmonic, it's frequency is just 10 times that of the fundamental for example.

Remember that the first harmonic is the fundemental frequency. The reason why the frequency of the others can be related to the fundemental frequency, is that these waves span over the same length, L. As the wavelength of the fundemental is two times the length, with frequency f, if you have one whole wavelength in the picture for the same length L, the frequency is 2f.

For a more rigorous view on this, recall this equation:

v = f \lambda

The velocity in any harmonics is a constant, hence

f \lambda

is a constant. In the second harmonic, your wavelength is equal to L, hence, half of the fundamentals wavelength. For

f \lambda

to be a constant, the frequency must double.

(edited 9 years ago)

Reply 9

A84

Original post by Phichi

v = f \lambda

The velocity in any harmonics is a constant, hence

f \lambda

is a constant. In the second harmonic, your wavelength is equal to L, hence, half of the fundamentals wavelength. For

f \lambda

to be a constant, the frequency must double.

Thanks,
Then um what is the difference between fundamental mode andfundamental frequency?

Reply 10

Phichi

Original post by A84

Thanks,
Then um what is the difference between fundamental mode andfundamental frequency?

They are equivalent. The fundamental oscillation mode is the case where the wavelength is twice the length of the string. Hence this is the fundamental frequency.