Sally Sue, an enthusiastic physics student enjoyed the opportunity to collect data from standing waves in a spring. She and her partner help the ends of their spring 4.00 meters apart. There are 5 nodes in the standing wave produced. Sally moved her hand from the rest position back and forth along the floor 20 times in 4.00 s.
a. the wavelength of the wave Sally Sue sent
b. the frequency of the wave produced
c. the speed of the wave
2.5 lambda for the total length
lamda= 4/2.5 meters
f= 20/4 hz
speed= f*lambda
To find the wavelength of the wave Sally Sue sent, we can use the formula:
Wavelength (λ) = Distance (d) / Number of Nodes (n)
Given:
Distance (d) = 4.00 meters
Number of Nodes (n) = 5
a. Wavelength (λ) = 4.00 meters / 5
Wavelength (λ) = 0.8 meters
Therefore, the wavelength of the wave Sally Sue sent is 0.8 meters.
To find the frequency of the wave produced, we can use the formula:
Frequency (f) = Number of Oscillations (N) / Time (t)
Given:
Number of Oscillations (N) = 20
Time (t) = 4.00 seconds
b. Frequency (f) = 20 / 4.00
Frequency (f) = 5 Hz
Therefore, the frequency of the wave produced is 5 Hz.
To find the speed of the wave, we can use the formula:
Speed (v) = Wavelength (λ) x Frequency (f)
Given:
Wavelength (λ) = 0.8 meters
Frequency (f) = 5 Hz
c. Speed (v) = 0.8 meters x 5 Hz
Speed (v) = 4 meters/second
Therefore, the speed of the wave is 4 meters/second.
To find the answers, we can use the formulas related to the properties of waves and the equation for the velocity of a wave. Here's how to find each value:
a. The wavelength of the wave Sally Sue sent:
The wavelength (λ) is the distance between two consecutive nodes (or antinodes). In this case, there are 5 nodes given, so we need to calculate the distance between them.
First, we need to find the total distance between the nodes. Since the spring is 4.00 meters long and there are 5 nodes, we can divide the length of the spring by the number of nodes:
Total distance = length / (number of nodes + 1)
Total distance = 4.00 m / (5 + 1) = 0.67 m
However, this distance is only half the wavelength because a full wavelength consists of a node and its adjacent antinode. So, we need to double this value to find the wavelength:
Wavelength (λ) = 2 * total distance = 2 * 0.67 m = 1.34 m
Therefore, the wavelength of the wave Sally Sue sent is 1.34 meters.
b. The frequency of the wave produced:
The frequency (f) represents the number of oscillations or cycles per second. In this case, Sally moved her hand back and forth along the floor 20 times in 4.00 seconds.
To find the frequency, we can use the formula:
Frequency (f) = Number of cycles / Time taken
Frequency (f) = 20 / 4.00 s = 5 Hz
Therefore, the frequency of the wave produced is 5 Hz.
c. The speed of the wave:
The speed of a wave (v) is given by the formula:
Speed (v) = Frequency (f) * Wavelength (λ)
Using the values we found previously, we can calculate the speed:
Speed (v) = 5 Hz * 1.34 m = 6.7 m/s
Therefore, the speed of the wave is 6.7 m/s.
A-1.6
B-5
C-3.125