[Python] Matplotlib slider not working when plot is updated in separate function

I am using matplotlib's Slider to do a simple dynamic plot of a sine curve. I want to change the frequency using a slider. The code looks like this:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider

x = np.linspace(400, 800, 400)

fig, ax = plt.subplots()
fig.subplots_adjust(bottom=0.25)
mod = 1.
lambda_plot, = ax.plot(x, np.sin(mod*x*2*np.pi/500))


ax_mod_slider = fig.add_axes([0.3, 0.1, 0.5, 0.04])
mod_slider = Slider(
ax = ax_mod_slider,
label = "modulation",
valmin = 0,
valmax = 20,
valinit = 1.,
orientation = "horizontal")

def update_mod(val):
mod = mod_slider.val
redraw()
fig.canvas.draw_idle()


def redraw():
lambda_plot.set_ydata(np.sin(mod*x*2*np.pi/500))


mod_slider.on_changed(update_mod)

plt.show()


This does only work if I put the code in redraw() directly in update_mod(), like this:

def update_mod(val):
mod = mod_slider.val
lambda_plot.set_ydata(np.sin(mod*x*2*np.pi/500))
fig.canvas.draw_idle()


Why can I not call another function for changing the plot? In this example, I could put it all into update_mod(), but as I do more complicated calculations, I thought it might be good to be able to split update_mod() into separate functions.

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