import numpy as np
import matplotlib.pyplot as plt

plt.rcParams['mathtext.fontset'] = 'cm'

high_pass_trans = lambda S, k, L, a: 1/(1 + ((np.pi*a**2)/(2*S*k*L))**2)
high_pass_cutoff = lambda S, c, L, a: c*a**2/(2*S*L)

c = 343.4
L = 0.06
S = 0.003
a = 0.015
fc = high_pass_cutoff(S, c, L, a)
freq = np.logspace(0, 4, 101)
k = 2 * np.pi * freq/c
T = high_pass_trans(S, k, L, a)
plt.semilogx(freq, T)
plt.text(140, 0.5,  "Cut-off frequency: {:g} Hz".format(fc))
plt.grid(which="both", alpha=0.4)
plt.xlabel("Frequency (Hz)")
plt.ylabel("$T_\pi$")
plt.title("High-pass filter for $S=30$ cm², $a=1.5$ cm")
plt.savefig("Acoustics filter highpass.svg")