A Level Physics Practice Exam

What is one of the conditions necessary for a stationary wave to form in a stretched string?

1. The string must be under tension

2. The string must be free to vibrate

3. The string must be a whole number of wavelengths long

4. The string must have an uneven mass distribution

The correct answer is: The string must be a whole number of wavelengths long

For a stationary wave to form in a stretched string, it is essential that the string has a specific physical length that accommodates whole wavelengths of the wave. This is because stationary waves, also known as standing waves, are produced when two waves traveling in opposite directions interfere with each other. In a stretched string, for constructive interference to occur at certain points, the length of the string must be equal to an integer multiple of half the wavelength. When the string supports a whole number of wavelengths, it creates nodes (points of no displacement) and antinodes (points of maximum displacement) at predictable locations. This arrangement allows the wave to be sustained without dissipating energy, leading to the characteristic patterns of a stationary wave. The other conditions, while important for wave behavior, do not independently ensure the formation of stationary waves. For example, while the string must be under tension and free to vibrate, these aspects alone do not guarantee that a stationary wave will be created in a specific length of string. Similarly, having an uneven mass distribution will disrupt rather than facilitate the formation of stationary waves, making it a less favorable condition for such waves. Thus, the requirement of having the string be a whole number of wavelengths long is critical for establishing a stable stationary wave