Interference of Waves
14.5 Interference of Waves
Learning Objectives
By the end of this section, you will be able to:
- Explain how mechanical waves are reflected and transmitted at the boundaries of a medium
- Define the terms interference and superposition
- Find the resultant wave of two identical sinusoidal waves that differ only by a phase shift
Practice!
| Practice 14.5.1 |
|---|
 A wave pulse with a positive displacement from equilibrium is traveling to the right in a string that is tied to a vertical support, as shown in the figure. What will happen when the pulse arrives at the end of the string? |
| (a) A reflected pulse will travel in the opposite direction with a displacement from equilibrium that alternates between positive and negative. |
| (b) A reflected pulse will travel in the opposite direction with a positive displacement from equilibrium. |
| (c) A reflected pulse will travel in the opposite direction with a negative displacement from equilibrium. |
| (d) The support will absorb the wave pulse and nothing will reflect. |
When the pulse arrives at the end of the string, a reflected pulse will travel in the opposite direction with a negative displacement from equilibrium. When the pulse arrives at the vertical support, it exerts an upward force on the support. The support then exerts a downward reaction force on the string that sets up a reflected pulse in the opposite direction, with opposite displacement.
Since the reaction force exerted by the support on the string in downward, or opposite to the force exerted by the string on the support, the reflected pulse will always has a displacement opposite to the incident pulse.
| Practice 14.5.2 |
|---|
 A wave pulse with a positive displacement from equilibrium is traveling to the right in a string that is tied to a ring that can freely slide up and down on a vertical rod, as shown in the figure. What will happen when the pulse arrives at the end of the string? |
| (a) The support will absorb the wave pulse and nothing will reflect. |
| (b) A reflected pulse will travel in the opposite direction with a displacement from equilibrium that alternates between positive and negative. |
| (c) A reflected pulse will travel in the opposite direction with a negative displacement from equilibrium. |
| (d) A reflected pulse will travel in the opposite direction with a positive displacement from equilibrium. |
When the pulse arrives at the end of the string, a reflected pulse will travel in the opposite direction with a positive displacement from equilibrium. When the pulse arrives at the ring, the ring can slide upward along the vertical rod. Tension in the string pulls the ring back downward and this sets up a reflected pulse in the opposite direction.
Since the ring is free to move up and down on the rod, it does not exert a downward reaction force on the string. This keeps the reflected wave pulse displacement in the same direction as the incident wave pulse displacement.
| Practice 14.5.3 |
|---|
 Two wave pulses travel in opposite directions and interfere when they arrive at the same position in space. One pulse, with an amplitude of 2 units, travels to the right while the other pulse, with an amplitude of 4 units, travels to the left, as shown in the figure. What is the amplitude of the resulting pulse when these two wave pulses interfere? |
| (a) 0 units |
| (b) 3 units |
| (c) 2 units |
| (d) 4 units |
| (e) 6 units |
When these two wave pulses interfere, the amplitude of the resulting wave pulse is 6 units. The total displacement of the resultant pulse that arises when the two pulses interfere (overlap) is the algebraic sum of the amplitudes of the two interfering pulses. The amplitude of the resultant pulse is 2 units + 4 units, which equals 6 units.
| Practice 14.5.4 |
|---|
 Two wave pulses travel in opposite directions and interfere when they arrive at the same position in space. One pulse, with an amplitude of 2 units, travels to the right while the other pulse, with an amplitude of -4 units, travels to the left, as shown in the figure. What is the amplitude of the resulting pulse when these two wave pulses interfere? |
| (a) -4 units |
| (b) -6 units |
| (c) 2 units |
| (d) -2 units |
| (e) 0 units |
When these two wave pulses interfere, the amplitude of the resulting wave pulse is -2 units. The total displacement of the resultant pulse that arises when the two pulses interfere (overlap) is the algebraic sum of the amplitudes of the two interfering pulses. The amplitude of the resultant pulse is 2 units + -4 units, which equals -2 units.
| Practice 14.5.5 |
|---|
 Two triangular wave pulses travel in opposite directions and interfere when they arrive at the same position in space. One pulse, with an amplitude of 1.00 cm, travels to the right at 2.00 cm/s while the other pulse, with an amplitude of 1.00 cm, travels to the left at 2.00 cm/s, as shown in the figure. What is the amplitude of the resulting pulse when these two wave pulses interfere? |
| (a) 1.50 cm |
| (b) 3.00 cm |
| (c) 0 cm |
| (d) 1.00 cm |
| (e) 2.00 cm |
When these two wave pulses interfere, the amplitude of the resulting wave pulse is 2.00 cm. The total displacement of the resultant pulse that arises when the two pulses interfere (overlap) is the algebraic sum of the amplitudes of the two interfering pulses. The amplitude of the resultant pulse is 1.00 cm + 1.00 cm, which equals -2.00 cm.
Physics Education Research at UNG 