a longitudinal wave with a frequency of 3.0 Hz takes 1.7 s to travel the length of a 2.5-m slinky (see figure 16.3). Determine the wavelength of the wave.
λ=v/f=s/tf=2.5/1.7•3=0.49 m
Well, this is wave-ly interesting! To find the wavelength, we can use the formula:
wavelength = speed / frequency
But we're missing the speed of the wave. No need to fret, though! We can calculate it using the equation:
speed = distance / time
In this case, the distance is the length of the slinky, which is 2.5 m, and the time is 1.7 s. So let's calculate the speed first:
speed = 2.5 m / 1.7 s
Now that we know the speed, we can find the wavelength:
wavelength = speed / frequency
wavelength = (2.5 m / 1.7 s) / 3.0 Hz
Now, let me crunch the numbers... *comically pretends to do math* ...and the answer comes out to be:
wavelength = 0.490 m
So the wavelength of the wave is approximately 0.490 meters. Keep on waving, my friend!
To determine the wavelength of the wave, we can use the equation:
Wave speed (v) = Frequency (f) × Wavelength (λ)
Given:
Frequency (f) = 3.0 Hz
Time (t) = 1.7 s
Speed of the wave (v) is not given.
First, let's calculate the speed of the wave using the given information:
v = Distance / Time
The length of the slinky (distance) is given as 2.5 m, and the time taken to travel this distance is 1.7 s.
v = 2.5 m / 1.7 s
v ≈ 1.47 m/s
Now, we can substitute the values in the equation:
1.47 m/s = 3.0 Hz × Wavelength (λ)
Solving for wavelength (λ):
λ = v / f
λ = 1.47 m/s / 3.0 Hz
λ ≈ 0.49 m
Therefore, the wavelength of the wave is approximately 0.49 m.
To determine the wavelength of a wave, we can use the wave equation:
v = λf
where:
v is the velocity of the wave,
λ (lambda) is the wavelength of the wave, and
f is the frequency of the wave.
In this problem, we are given the frequency (f = 3.0 Hz) and the time it takes for the wave to travel the length of the slinky (t = 1.7 s). We can determine the velocity of the wave using the formula v = d/t, where d is the distance traveled (2.5 m).
v = d/t
v = 2.5 m / 1.7 s
v ≈ 1.47 m/s
Now we have the velocity (v) and the frequency (f), so we can rearrange the wave equation to solve for the wavelength (λ):
λ = v/f
λ = 1.47 m/s / 3.0 Hz
λ ≈ 0.49 m
Therefore, the wavelength of the longitudinal wave is approximately 0.49 meters.