Answer :
To determine how far the wave would travel in 6.000 seconds, we need to follow a systematic approach:
1. Identify the given information:
- Wavelength ([tex]\(\lambda\)[/tex]) = 0.25 meters
- Frequency ([tex]\(f\)[/tex]) = 2.0 Hz
- Time ([tex]\(t\)[/tex]) = 6.000 seconds
2. Calculate the speed of the wave:
The speed ([tex]\(v\)[/tex]) of a wave is given by the product of its wavelength ([tex]\(\lambda\)[/tex]) and its frequency ([tex]\(f\)[/tex]):
[tex]\[ v = \lambda \times f \][/tex]
Substituting the given values:
[tex]\[ v = 0.25 \, \text{meters} \times 2.0 \, \text{Hz} \][/tex]
[tex]\[ v = 0.50 \, \text{meters/second} \][/tex]
3. Calculate the distance traveled by the wave:
The distance ([tex]\(d\)[/tex]) traveled by the wave in a given time ([tex]\(t\)[/tex]) is found by multiplying the speed ([tex]\(v\)[/tex]) by the time ([tex]\(t\)[/tex]):
[tex]\[ d = v \times t \][/tex]
Substituting the calculated wave speed and given time:
[tex]\[ d = 0.50 \, \text{meters/second} \times 6.000 \, \text{seconds} \][/tex]
[tex]\[ d = 3.00 \, \text{meters} \][/tex]
Thus, the wave travels 3.00 meters in 6.000 seconds. The correct answer is not among the provided options, as it should be:
C. 3.00m
1. Identify the given information:
- Wavelength ([tex]\(\lambda\)[/tex]) = 0.25 meters
- Frequency ([tex]\(f\)[/tex]) = 2.0 Hz
- Time ([tex]\(t\)[/tex]) = 6.000 seconds
2. Calculate the speed of the wave:
The speed ([tex]\(v\)[/tex]) of a wave is given by the product of its wavelength ([tex]\(\lambda\)[/tex]) and its frequency ([tex]\(f\)[/tex]):
[tex]\[ v = \lambda \times f \][/tex]
Substituting the given values:
[tex]\[ v = 0.25 \, \text{meters} \times 2.0 \, \text{Hz} \][/tex]
[tex]\[ v = 0.50 \, \text{meters/second} \][/tex]
3. Calculate the distance traveled by the wave:
The distance ([tex]\(d\)[/tex]) traveled by the wave in a given time ([tex]\(t\)[/tex]) is found by multiplying the speed ([tex]\(v\)[/tex]) by the time ([tex]\(t\)[/tex]):
[tex]\[ d = v \times t \][/tex]
Substituting the calculated wave speed and given time:
[tex]\[ d = 0.50 \, \text{meters/second} \times 6.000 \, \text{seconds} \][/tex]
[tex]\[ d = 3.00 \, \text{meters} \][/tex]
Thus, the wave travels 3.00 meters in 6.000 seconds. The correct answer is not among the provided options, as it should be:
C. 3.00m
To find how far the wave travels, calculate its speed using the given wavelength and frequency, then multiply that speed by the given time. The wave travels 3.0 meters in 6.000 seconds.
To determine how far a water wave would travel, we first need to understand the relationship between wavelength, frequency, and the speed of the wave.
The speed of a wave (v) is given by the product of its wavelength (λ) and frequency (f). Therefore: v = f × λ
Given:
- Wavelength (λ) = 0.25 m
- Frequency (f) = 2.0 Hz
First, we calculate the speed of the wave:
v = 2.0 Hz × 0.25 m = 0.5 m/s
Next, we determine the distance the wave would travel in 6.000 seconds. The distance (d) is calculated by multiplying the speed of the wave by the time interval (t): d = v × t
Using the given time interval of 6.000 seconds:
d = 0.5 m/s × 6.000 s = 3.0 m
The correct answer is neither 0.75m nor 1.5m, but actually 3.0m.
