To determine how long it takes the wave to travel 6.0 meters in the x-direction, we first need to find the wave's speed.
The general formula for wave speed (\(v\)) is given by:
\[ v = f \lambda \]
where:
- \(f\) is the frequency of the wave,
- \(\lambda\) is the wavelength.
From the graph, we can observe the wave completes one full cycle (crossing the x-axis back to the same position) every 1 second. This means the frequency \(f\) is 1 Hz.
Given that the wavelength (\(\lambda\)) is 1.5 m, we can now calculate the wave speed:
\[ v = f \lambda = 1 , \text{Hz} \times 1.5 , \text{m} = 1.5 , \text{m/s} \]
Now that we have the wave speed, we can determine the time it takes for the wave to travel 6.0 m using the formula:
\[ \text{time} = \frac{\text{distance}}{\text{speed}} \]
Substituting in the values:
\[ \text{time} = \frac{6.0 , \text{m}}{1.5 , \text{m/s}} = 4.0 , \text{s} \]
It appears that 4.0 seconds is not on the list of choices provided, indicating a mismatch. Let’s clarify that the calculation was performed correctly.
Rechecking based on the context or any potential disparity between distance and the period of wave behavior confirms that the frequency and wavelength lead us to a speed of 1.5 m/s.
As earlier noted, the wave crosses the x-axis every second, indicating seconds relate to cycles more than to propagation per-se.
Given the options:
- 0.13 seconds
- 0.67 seconds
- 2.0 seconds
- 8.0 seconds
None matches our calculated travel time of 4 seconds. Thus, if options are strictly adhered to without actual distance or velocity clarifications beyond visible increments, none conclude this scenario perfectly.
As calculated correctly, to travel a whole 6 meters definitively affirms necessary times longer than what’s presented in solutions. From evaluation perspective could be wrongly contextualized on the question detailing as options suggest intervals far shorter than required aforementioned determination definitely at 4 seconds.
Yet, be noted, if approximation or reframing into doubling traveled sections, roughly to realign fractions, was required into criteria, something interpolating 2 seconds might emerge tested via ironically 1.5 m/s propelling indirect placements contrasted faster intervals but still facing challenges nominally.
Unfortunately, either re-evaluation or explicitly alternate outcomes remain skewed from actual foundational assessment plus select concrete calculation stipulations.
To conclude based on literal resolutions:
The time taken for the wave to travel 6.0 m is indeed 4.0 seconds, not aligned with present alternatives.
1 answer