Question:

A student is given a slinky and asked to investigate wave characteristics. They decide to measure the wavelength and frequency of a wave by creating a standing wave. The student holds one end of the slinky and moves it up and down at a frequency of 2.5 Hz, while the other end is anchored to a support. The distance between two consecutive nodes in the standing wave is measured to be 0.8 m.

1. What is the wavelength of the wave?
2. What is the speed of the wave?
3. What is the amplitude of the wave?

Answer:

1. The wavelength of the wave can be determined by the distance between two consecutive nodes. In a standing wave, nodes are points of zero displacement. The distance between two consecutive nodes is half a wavelength, so:

   Wavelength = 2 * Distance between nodes = 2 * 0.8 m = 1.6 m

   Therefore, the wavelength of the wave is 1.6 m.

2. To find the speed of the wave, we can use the formula:

   Speed = Wavelength * Frequency

   Given that the frequency is 2.5 Hz and the wavelength is 1.6 m:

   Speed = 1.6 m * 2.5 Hz = 4 m/s

   Therefore, the speed of the wave is 4 m/s.

3. The amplitude of the wave is the maximum displacement from the equilibrium position. In this case, the amplitude can be determined by the maximum vertical distance the student moves the slinky up and down. Since the question does not provide this information, we cannot determine the amplitude with the given data.

   Therefore, the amplitude of the wave is unknown based on the given data.

In summary:

1. The wavelength of the wave is 1.6 m.
2. The speed of the wave is 4 m/s.
3. The amplitude of the wave is unknown based on the given data.