By shaking one end of a stretched string, a single pulse is generated. The traveling pulse carries

1. mass.

2. energy.

3. momentum.

4. energy and momentum.

5. mass and energy.

6. all three.

7. neither of the three.

Explanation: A traveling wave does not involve any transport of mass (even though mass gets displaced, no mass actually travels along with the wave from one point in space to another). By shaking one end of a rope, however, one can get the other end to move, and when that end is put in motion, it has both momentum and energy. So when the wave travels down the rope, it carries both momentum and energy.

What can be said about the speed of a particle in a uniform medium through which a wave travels and the speed of the wave?

1. The motion of the wave and a particle in the medium are always perpendicular.

2. The speed of the wave varies but the speed of the particle does not.

3. The speed of the particle varies but the speed of the wave does not.

4. Both speeds are constant.

5. The two are completely unrelated.

Explanation: The speed of a wave is a constant through a uniform medium. The speed of the particles of the medium is constantly changing because they are undergoing simple harmonic motion. The two speeds are not necessarily perpendicular depending on whether the wave is transverse or longitudinal.

Choose the correct answer(s). Two different continuous waves on the surface of a pond would be expected to have roughly the same

1. wavelengths.

2. wave speeds.

3. frequencies.

4. energies.

5. amplitudes.

6. none of these.

Explanation: The wave speed will be roughly the same for all waves on the pond surface since this property is principally determined by the medium through which the wave travels. The other quantities can be varied by the specific manner in which the waves are created.

Explanation: The left end of the long spring (point P) is displaced toward the right and kept there. The displacement s of point P is therefore nonzero. Only graphs 3 and 5 show a nonzero displacement at the left. At the instant shown, the wave pulse has not yet been displaced. Graph 5 shows a negative displacement at the right end, so the only possible choice is graph 3.

Explanation: A traveling wave does not involve any transport of mass (even though mass gets displaced, no mass actually travels along with the wave from one point in space to another.) By shaking one end of a rope, however, one can get the other end to move, and when that end is put into motion, it has both energy and momentum. So when the wave travels down the rope, it carries both momentum and energy.

The correct answers are: A and C.

Explanation: Choice A is correct because, when the two pulses are in the same position, they cancel each other exactly, leaving the string completely straight. Choice C is only correct since the point right in the middle between the two pulses cannot move–whatever the displacement due to one pulse at that point, it is canceled by the displacement due to the other.

Explanation: First the shallow side of the pulse moves through P, then the steep side. So the displacement increases more slowly than it decreases. Note that diagram 1 and 3 do not represent a physically possible situation: In both instances, the diagram indicates more than one possible value of displacement at a given instant.

Explanation: The following diagram shows the string just before (top) and just after (bottom) it reaches position b (middle). Dot R moves downward just before the string reaches position b and upward just afterwards. The instantaneous velocity of the dot right at b, therefore is zero. Similarly, the instantaneous velocity of dot P is zero and since dot Q doesn’t move at all, its instantaneous velocity, too, is zero.