Which one of the following will form a standing wave: (1) two waves of the same amplitude and speed moving in the same direction (2) two waves of the same amplitude and speed moving in the opposite directions, (3) any two traveling waves can form standing wave if they have same amplitude (4) any two traveling waves can form standing wave if they have same energy
From what I've read in my textbook, I believe the answer is (2). Is this correct. Thank you in advance.
(2) Same amplitude, opposite directions.
To determine which option will form a standing wave, let's understand the concept of standing waves and how they are formed.
Standing waves are formed when two waves with the same frequency, wavelength, and amplitude interact with each other. These waves superpose and create regions of constructive and destructive interference, resulting in a stationary pattern.
Now let's analyze the options:
(1) Two waves of the same amplitude and speed moving in the same direction:
When the waves have the same amplitude and speed while moving in the same direction, they will create a beat pattern, but not a standing wave. The beat pattern consists of regions of constructive and destructive interference that move along with the waves.
(2) Two waves of the same amplitude and speed moving in opposite directions:
When waves with the same amplitude and speed move in opposite directions, they create regions of constructive and destructive interference that remain fixed in space. These regions form standing wave patterns. This is the correct answer.
(3) Any two traveling waves can form a standing wave if they have the same amplitude:
This option is incorrect since having the same amplitude alone is not sufficient to form a standing wave. The waves must also have the same frequency, wavelength, and be moving in opposite directions.
(4) Any two traveling waves can form a standing wave if they have the same energy:
This option is incorrect because standing waves are formed based on the properties of the waves, such as frequency, wavelength, and amplitude, rather than energy.
Therefore, the correct option is (2) - two waves of the same amplitude and speed moving in opposite directions.