In Figure below the hand moves the end of the Slinky up and down through two complete cycles in one second. The wave moves along the Slinky at a speed of 0.545 m/s. Find the distance between two adjacent crests on the wave.
v = f (lambda) so lambda = v/f.
f is two cycles per second (Hz).
To find the distance between two adjacent crests on the wave, we need to find the wavelength.
The wavelength (λ) is the distance between two consecutive crests or troughs in a wave.
We know the speed of the wave (v) is 0.545 m/s and the time period (T) is 1 second.
The formula relating speed, wavelength, and time period is:
v = λ/T
Rearranging the formula, we get:
λ = v * T
Substituting the given values into the formula, we have:
λ = 0.545 m/s * 1 s
λ = 0.545 m
So, the distance between two adjacent crests on the wave is 0.545 meters.
To find the distance between two adjacent crests on the wave, we need to determine the wavelength of the wave.
The wavelength (λ) is the distance between two identical points on a wave, such as two adjacent crests or two adjacent troughs.
In this case, we are given the wave speed (v) of 0.545 m/s. The wave speed is given by the equation:
v = λ * f
Where:
v = wave speed
λ = wavelength
f = frequency
We know that the hand moves the end of the Slinky up and down through two complete cycles in one second, so the frequency (f) is 2 Hz (cycles per second).
Let's substitute these values into the equation:
0.545 m/s = λ * 2 Hz
Now, we can solve for the wavelength (λ):
λ = 0.545 m/s / 2 Hz
= 0.2725 m
Therefore, the distance between two adjacent crests on the wave is 0.2725 meters.