Suppose the amplitude and frequency of a transverse wave are, respectively, 1.3cm and 5.0Hz. Find the total vertical distance (in cm) through a fixed point in 3.0s.
PLEASE GIVE ME SOME IDEAS TO DO IT!!!THANKS A LOT!!!!!!!
I am somewhat bewildered about the term vertical distance. The wave is NOT moving vertically, but horizontally. The wave has amplitude vertically, but does not move vertically as it moves. Now if you look at one point only, as the wave sweeps by, the vertical amplitude changes as various points of the wave pass the point. If you are asking how much the vertical amplitude changes, then...
The amount of vertical change depends on the starting ampltitude. Look at it in degrees of wave motion.
period=.2seconds. Osciallation is 3 seconds, or 15 periods, exactly. The starting point is exactly the ending point. The vertical amplitude goes through a max of 1.3 to a min of 1.3, and back. So the vertical change, without regard to direction, is 5.2cm per period, or a total of 15 times that.
check my thinking.
For the vertical change, why is it 5.2cm per period?Shouldn't it be 2.6cm?
To find the total vertical distance through a fixed point in 3.0s, we can calculate the displacement of the wave over this time period. Here's a step-by-step solution:
Step 1: Determine the formula for the displacement of a transverse wave.
The formula for the displacement of a transverse wave is given by:
Displacement = Amplitude * sin(2π * Frequency * Time)
Step 2: Plug in the given values.
In this case, the amplitude (A) is 1.3 cm, the frequency (f) is 5.0 Hz, and the time (t) is 3.0 s. So, the formula becomes:
Displacement = 1.3 cm * sin(2π * 5.0 Hz * 3.0 s)
Step 3: Calculate the expression inside the sine function.
Multiplying the frequency and time, we get: 2π * 5.0 Hz * 3.0 s = 30π
Step 4: Evaluate the sine function.
Using a calculator, evaluate sin(30π). The result is approximately 0.945.
Step 5: Calculate the displacement.
Multiply the amplitude by the result from Step 4:
Displacement = 1.3 cm * 0.945 ≈ 1.24 cm
Therefore, the total vertical distance through the fixed point in 3.0s is approximately 1.24 cm.
To find the total vertical distance through a fixed point in 3.0 seconds, you can use the equation for the displacement of a transverse wave:
Displacement (y) = Amplitude × sin(2π × frequency × time)
Given:
Amplitude (A) = 1.3 cm
Frequency (f) = 5.0 Hz
Time (t) = 3.0 s
First, calculate the angular frequency (ω) using the formula:
Angular frequency (ω) = 2π × frequency
Next, calculate the displacement (y) using the equation mentioned above:
y = A × sin(ω × t)
Substituting the given values:
y = 1.3 × sin((2π × 5.0) × 3.0)
Now we can calculate the value of y.