Two transverse waves travel along the same taut string. Wave 1 is described by y1(x, t) = A sin(kx - ωt), while wave 2 is described by y2(x, t) = A sin(kx + ωt + φ). The phases (arguments of the sines) are in radians, as usual, and A = 2.1 cm and φ = 0.35π rad.
Choose the answer that correctly describes the waves’ directions of travel.
MultipleChoice :
1) Both waves travel in the negative x direction.
2) Due to the φ term in the phase of wave 2, it does not travel. Wave 1 travels in the negative x-direction.
3) Due to the φ term in the phase of wave 2, it does not travel. Wave 1 travels in the positive x-direction.
4) Both waves travel in the positive x-direction.
5) Wave 1 travels in the negative x-direction, while wave 2 travels in the positive x-direction.
6) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.
7) There is not enough information.
Solved
Show answers
More tips
- C Computers and Internet How to Create a Website for Free and Easy?...
- O Other Everything You Need to Know About Kudyabliks...
- C Computers and Internet The Twitter Phenomenon: What it is and How to Use it...
- C Computers and Internet How to Choose a Laptop: Expert Guide and Tips...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- C Computers and Internet How to Learn to Type Fast?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
Ответ:
6) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.
Explanation:
What matters is the part
, the other parts of the equation don't affect time and space variations. We know that when the sign is - the wave propagates to the positive direction while when the sign is + the wave propagates to the negative direction, but here is an explanation of this:
For both cases, + and -, after a certain time
(
), the displacement y of the wave will be determined by the
term. For simplicity, if we imagine we are looking at the origin (x=0), this will be simply
.
To know which side, right or left of the origin, would go through the origin after a time
(and thus know the direction of propagation) we have to see how we can achieve that same displacement y not by a time variation but by a space variation
(we would be looking where in space is what we would have in the future in time). The term would be then
, which at the origin is
. This would mean that, when the original equation has
, we must have that
for
to be equal to
, and when the original equation has
, we must have that
for
to be equal to ![kx-\omega \delta t](/tpl/images/0515/9126/5cd0e.png)
Note that their values don't matter, although they are a very small variation (we have to be careful since all this is inside a sin function), what matters is if they are positive or negative and as such what is possible or not .
In conclusion, when
, the part of the wave on the positive side (
) is the one that will go through the origin, so the wave is going in the negative direction, and viceversa.
Ответ:
One group of fabric is treated with the chemical, and the other group is not. Then each group is exposed to water.
Explanation: