Enchong is playing with a rope tied to a vertical post, such that waves on the rope move at a rate of 0.720 m/s. He discovers frequencies at which he can oscllate his end of the rope so that a point 45.0 em from the post does not move. What are these frequencies (expressed as multiples of integer n)?
To determine the frequencies at which a point 45.0 cm from the post does not move, we need to consider the wavelength and speed of the waves on the rope.
We can use the wave equation v = λf, where v is the speed of the wave, λ is the wavelength, and f is the frequency.
Given that the speed of the wave is 0.720 m/s, we can rearrange the equation to solve for the wavelength: λ = v/f.
We know that the point 45.0 cm from the post does not move, which means it corresponds to a node in the standing wave pattern. In a standing wave pattern, the distance between two nodes is half a wavelength.
Let's calculate the wavelength first:
Distance between two nodes = λ/2 = 45.0 cm = 0.45 m
λ/2 = 0.45 m
λ = 2 * 0.45 m
λ = 0.9 m
Now, we can calculate the frequencies using the wave equation:
f = v/λ
f = 0.720 m/s / 0.9 m
f = 0.8 Hz
So the frequency at which a point 45.0 cm from the post does not move is 0.8 Hz.
However, the question asks for the frequencies expressed as multiples of integer n, which means we need to find other frequencies that satisfy the same condition.
We can find these frequencies by multiplying the initial frequency by different integers (n). Let's find the values of n:
n = 1: f = 0.8 Hz * 1 = 0.8 Hz
n = 2: f = 0.8 Hz * 2 = 1.6 Hz
n = 3: f = 0.8 Hz * 3 = 2.4 Hz
n = 4: f = 0.8 Hz * 4 = 3.2 Hz
...
So the frequencies expressed as multiples of integer n are: 0.8 Hz, 1.6 Hz, 2.4 Hz, 3.2 Hz, and so on.