Today’s date is January 21st, 2021

Combined sine, adjust phase and frequency

Make a plot_ly plot, combining two sine waves with nearby frequencies through multiplcation. Give controls over the phase of the second sine wave. See what it does to the result.

Trig identity:

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

Rearranged:

sin(α) sin(β) = cos(α) cos(β) + cos(α + β)

So if one wave has frequency of 1 Hz, and other 2 Hz, what does phase do to signal?

Actually Plot_ly plots have all data evaluated ahead of time, with the controls only determining what data gets called upon.

For a good example, look here: https://plotly.com/r/sliders/

library(plotly)
## Loading required package: ggplot2
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
x <- seq(0,10, length.out = 2000)
y1 <- sin(2*pi*1*x)

#freqs <- seq(from=0.25, to =  5, by = 0.5)
phase <- seq(from = 0, to = 2*pi, by = 2*pi/16)
# create data
aval <- list()
p_ind <- 0
for(p in phase){
        p_ind <- p_ind + 1
        y2=sin(2*pi*2*x + p)
        aval[[p_ind]] <-list(visible = FALSE,
                            name = paste0('p = ', p),
                            x=x,
                            y=y1*y2)
}
aval[3][[1]]$visible = TRUE  #make the 3rd phase visible, the default slider step

Create the plot

See how all the lines are added through add_lines inside the for loop.

# create steps and plot all traces
steps <- list()
fig <- plot_ly()
for (i in 1:length(aval)) {
        fig <- add_lines(fig,x=aval[i][[1]]$x,  y=aval[i][[1]]$y, visible = aval[i][[1]]$visible, 
                         name = aval[i][[1]]$name, type = 'scatter', mode = 'lines', hoverinfo = 'name', 
                         line=list(color='00CED1'), showlegend = FALSE)
        
        step <- list(args = list('visible', rep(FALSE, length(aval))),
                     method = 'restyle',
                     label = phase[i])
        step$args[[2]][i] = TRUE  
        steps[[i]] = step 
}

Add the slider

fig <- fig %>%
        layout(title = "y = sin(1 Hz)*sin(2 Hz + phase)",
               sliders = list(list(active = 3,
                                   currentvalue = list(prefix = "Phase: "),
                                   steps = steps)))

fig #show the plot