The Motion of Dots on a String in a Transverse Wave
A transverse wave travels along a string
Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q.
i. The figure below shows the string at an instant in time. At the instant shown, dot P has maximum displacement and dot Q has zero displacement from equilibrium. At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous velocity of that dot. If either dot has zero velocity, write "v=0" next to the dot.
ii. The figure below shows the string at the same instant as shown in part (a)i. At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous acceleration of that dot. If either dot has zero acceleration, write "a=0" next to the dot.
Final answer:
Dot P has zero velocity at maximum displacement, while dot Q has maximum velocity directed to the right when it is at equilibrium. Dot P has maximum acceleration towards equilibrium, and dot Q has zero acceleration at equilibrium.
Explanation:
In addressing the scenario where a transverse wave travels along a string and we examine the motion of two dots labeled P and Q, we analyze their velocities and accelerations at a specific instant. For dot P, which is at maximum displacement, its instantaneous velocity is zero (v=0) because it is momentarily at rest as it changes direction from moving upward to moving downward. For dot Q, which has zero displacement, its velocity is at maximum, pointing in the direction of wave travel, which is to the right if the wave moves to the right.
Regarding accelerations, dot P would have maximum acceleration pointing towards the equilibrium position because it is at its extreme position. Dot Q would have zero acceleration (a=0) because it's at equilibrium and the acceleration at this point is zero.
2. A transverse wave travels to the right along a string. (a) Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q. i. The figure below shows the string at an instant in time. At the instant shown, dot P has maximum displacement and dot Q has zero displacement from equilibrium. At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous velocity of that dot. If either dot has zero velocity, write "v=0" next to the dot. ii. The figure below shows the string at the same instant as shown in part (a)i. At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous acceleration of that dot. If either dot has zero acceleration, write "a=0 " next to the dot. Final answer: Dot P has zero velocity at maximum displacement, while dot Q has maximum velocity directed to the right when it is at equilibrium. Dot P has maximum acceleration towards equilibrium, and dot Q has zero acceleration at equilibrium. Explanation: In addressing the scenario where a transverse wave travels along a string and we examine the motion of two dots labeled P and Q, we analyze their velocities and accelerations at a specific instant. For dot P, which is at maximum displacement, its instantaneous velocity is zero (v=0) because it is momentarily at rest as it changes direction from moving upward to moving downward. For dot Q, which has zero displacement, its velocity is at maximum, pointing in the direction of wave travel, which is to the right if the wave moves to the right. Regarding accelerations, dot P would have maximum acceleration pointing towards the equilibrium position because it is at its extreme position. Dot Q would have zero acceleration (a=0) because it's at equilibrium and the acceleration at this point is zero.