Sally and a partner holds the ends of a spring 4 meters apart. There are 5 nodes in the standing wave produced. Sally moves her hand from the rest position back and forth along the floor 20 times in 4 seconds.

Determine the following:
Wavelenght of wave sally sue sent
Frequence of wave produced
Speed of wave

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To determine the wavelength, frequency, and speed of the wave, we need to use the formulas related to the properties of waves.

1. Wavelength (λ): The wavelength is the distance between two consecutive identical points in a wave, such as two adjacent nodes or two adjacent crests.

In this case, we are given that there are 5 nodes in the standing wave produced. The distance between the ends of the spring is 4 meters. The number of nodes from one end to the other should be 5 - 1 = 4.

Therefore, the wavelength (λ) of the wave is the distance (4 meters) divided by the number of nodes between the ends:
λ = 4 meters / 4 nodes = 1 meter

So, the wavelength of the wave is 1 meter.

2. Frequency (f): The frequency of a wave is the number of complete cycles or oscillations per second. It is usually measured in Hertz (Hz).

In the problem, it is given that Sally moves her hand back and forth along the floor 20 times in 4 seconds. This represents one complete cycle of the wave.

Therefore, the frequency (f) of the wave is the number of cycles per second:
f = 20 cycles / 4 seconds = 5 Hz

So, the frequency of the wave is 5 Hz.

3. Speed of the wave (v): The speed of a wave is given by the formula v = f × λ, where v is the speed, f is the frequency, and λ is the wavelength.

Substituting the given values, we can calculate the speed of the wave:
v = 5 Hz × 1 meter = 5 meters/second

So, the speed of the wave is 5 meters/second.

Thus, the answers to the given questions are:
- Wavelength: 1 meter
- Frequency: 5 Hz
- Speed: 5 meters/second