Waves on a string

README.md

An experiment with using pygame to simulate a physical system, inspired by Peter Collingridges's tutorial posts. In this case, I'm modelling resonances on a string fixed at one end, with the other end driven at a variable frequency. Full description in blog post here.

standingwave.py

## Standing wave demonstration with pygame
 
import pygame
import time
import math
 
# Window size
canvas_width = 640
canvas_height = 480
 
# Define colours
line_colour = pygame.Color(55, 115, 212, 0)
background_colour = pygame.Color(255, 255, 255, 0)
slider_colour = pygame.Color(0, 0, 0, 0)
 
 
# Make screen
screen = pygame.display.set_mode((canvas_width, canvas_height))
screen.fill(background_colour)
 
# Make drawing surface
surface = pygame.Surface((canvas_width, canvas_height)).convert()
surface.fill(background_colour)
 
# Define standing wave function
 
amplitude = 3 # in px
speed = 1
 
def k(n):
    return n*math.pi/canvas_width
 
def ysummand(x, n, frequency):
    return ((float(frequency)/speed)**2/n)*(1/(k(n)**2-(float(frequency)/speed)**2))*math.sin(k(n)*(float(x)))
 
def ysum(x, Nmax, frequency):
    sumList = [0]*Nmax
    for i in range(1, Nmax):
        sumList[i] = ysummand(x, i, frequency)
 
    return sum(sumList)
 
def y(x, frequency):
    return (2/math.pi)*amplitude*ysum(x, 10, frequency)
 
def psi(x, frequency):
    return y(x, frequency) + amplitude*(1 - (float(x)/float(canvas_width)))
 
 
 
 
pygame.init()
 
# Main loop
running = True
 
freq = 0.01 # set initial frequency
 
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False
 
    # Redraw background
    surface.fill(background_colour)
 
    for xrange in range(0, canvas_width):
    yrange = int((canvas_height/2) + psi(xrange, freq)*math.cos(1000*speed*freq*time.time()))
    for i in range(0, 4):
        surface.set_at((xrange, yrange + i), line_colour)
 
    # Display some text
    font = pygame.font.Font(None, 36)
    text = font.render("Frequency is "+str(abs(freq)), 1, (10, 10, 10))
    textpos = text.get_rect()
    textpos.centerx = surface.get_rect().centerx
    surface.blit(text, textpos)
 
    move_ticker = 0
    keys=pygame.key.get_pressed()
    if keys[pygame.K_LEFT]:
        if move_ticker == 0:
            move_ticker = 20
            freq -= 0.0001
    if keys[pygame.K_RIGHT]:
        if move_ticker == 0:   
            move_ticker = 20    
            freq += 0.0001
 
 
 
 
    # Add surface to screen
    screen.blit(surface, (0, 0))
 
    # Display 
    pygame.display.flip()
 
 
 
pygame.quit()