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

The distance between nodes of the standing wave pattern is a half wavelength. Therefore the wavelength is 2*4m/5 = 1.6m

The frequency of the traveling waves is 20/4 = 5 Hz

Wave speed = wavelength * frequency
= __ m/s

Well, Sally and her partner must have quite the spring fling going on! Let's dive into these calculations with a touch of humor, shall we?

To determine the wavelength (λ) of the wave Sally Sue sent, we can use the formula:
λ = (2 x Length of spring) / Number of nodes.

Given that the ends of the spring are held 4 meters apart, we find:
λ = (2 x 4 m) / 5 = 1.6 meters.

Now, let's move on to the frequency (f) of the wave produced. We can use the formula:
f = Number of oscillations / Time taken.

Since Sally Sue moves her hand back and forth 20 times in 4 seconds, we find:
f = 20 / 4 = 5 Hz.

Lastly, the speed (v) of the wave can be calculated using the formula:
v = λ x f.

Plugging in our values, we have:
v = (1.6 m) x (5 Hz) = 8 m/s.

So, Sally Sue sent a wave with a wavelength of 1.6 meters, a frequency of 5 Hz, and the wave traveled at a speed of 8 m/s. That's some springy fun!

To determine the wavelength of the wave, we need to count the number of nodes. In a standing wave, a node is a point where the displacement of the wave is always zero. Since there are 5 nodes in the standing wave, the wavelength is equal to the distance between consecutive nodes.

Given that Sally and her partner are holding the ends of the spring 4 meters apart, the distance between consecutive nodes is the distance between the two partners divided by one less than the number of nodes:

Distance between nodes = Distance between partners / (Number of nodes - 1)

Distance between nodes = 4 m / (5 - 1)

Distance between nodes = 4 m / 4

Distance between nodes = 1 meter

Therefore, the wavelength of the wave Sally sent is 1 meter.

To determine the frequency of the wave produced, we need to find the number of oscillations or back and forth movements Sally's hand makes in a given time period.

Given that Sally moves her hand from the rest position back and forth along the floor 20 times in 4 seconds, the frequency is calculated by dividing the number of oscillations by the time period:

Frequency = Number of oscillations / Time period

Frequency = 20 oscillations / 4 seconds

Frequency = 5 Hz

Therefore, the frequency of the wave produced is 5 Hz.

To determine the speed of the wave, we use the formula:

Speed = Frequency x Wavelength

Given that the frequency is 5 Hz and the wavelength is 1 meter, the speed of the wave is:

Speed = 5 Hz x 1 m

Speed = 5 m/s

Therefore, the speed of the wave is 5 m/s.

To determine the wavelength, frequency, and speed of the wave produced by Sally, we can use the formulas:

1. Wavelength (λ) = Distance between two consecutive nodes
2. Frequency (f) = Number of complete cycles (oscillations) per second
3. Speed (v) = Wavelength (λ) × Frequency (f)

Given information:
- The distance between Sally and her partner is 4 meters, which corresponds to the distance between two consecutive nodes in the standing wave.
- There are 5 nodes in the standing wave, so there are 4 intervals between them (counting from one end to the other).
- Sally's hand moves back and forth along the floor 20 times in 4 seconds.

Now let's calculate the values step by step.

1. Wavelength (λ):
The distance between two consecutive nodes is 4 meters. As there are 5 nodes, there are 4 intervals between them. So the wavelength can be found by dividing the total distance by the number of intervals:
Wavelength (λ) = 4 meters / 4 intervals
Wavelength (λ) = 1 meter

2. Frequency (f):
Frequency is the number of complete cycles (oscillations) per second. Sally's hand moves back and forth along the floor 20 times in 4 seconds. To find the frequency, we divide the number of cycles by the time period:
Frequency (f) = 20 cycles / 4 seconds
Frequency (f) = 5 cycles/second or 5 Hz

3. Speed (v):
Speed is given by the formula v = λ × f, where v is the speed, λ is the wavelength, and f is the frequency. Using the values we calculated:
Speed (v) = 1 meter (wavelength) × 5 cycles/second (frequency)
Speed (v) = 5 meters/second

Therefore, the answers are:
- Wavelength of the wave Sally sent: 1 meter
- Frequency of the wave produced: 5 Hz
- Speed of the wave: 5 meters/second