Problem 11 IYPT 2027: 11. Sound isolation

Problem Description & Analysis

The sound isolation of a room may become breached if the door is not shut properly, even if the gap is negligibly small. Investigate how the shape and size of a small opening affect the transmission of sound.

Interactive Simulation (Python)

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جرم سطحی σ (kg/m²) 5 kg/m²

فرکانس کمینه (Hz) 100 Hz

فرکانس بیشینه (Hz) 5000 Hz

زاویهٔ برخورد (°) 0 °

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Python Code Lab

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Python — Editable

# آزمایش عایق‌بندی صوتی — TL برحسب فرکانس برای دو مادهٔ مختلف
import numpy as np
import matplotlib.pyplot as plt

rho_c = 415.0

# --- بخش ۱: داده‌های شما ---
# فرکانس‌های آزمایش (Hz)
f_Hz = np.array([125, 250, 500, 1000, 2000, 4000])
# نمونهٔ ۱: مقوا (σ ≈ 0.8 kg/m²)
TL_cardboard = np.array([6, 11, 17, 22, 28, 34])
# نمونهٔ ۲: صفحهٔ گچی (σ ≈ 10 kg/m²)
TL_gypsum    = np.array([21, 27, 33, 39, 45, 51])

# --- بخش ۲: نظریه ---
def mass_law(f, sigma):
    return 10*np.log10(1 + (2*np.pi*f*sigma/(2*rho_c))**2)

TL1_th = mass_law(f_Hz, 0.8)
TL2_th = mass_law(f_Hz, 10.0)

# --- بخش ۳: نمودار ---
fig, ax = plt.subplots(figsize=(8, 4.8))
f_sm = np.logspace(np.log10(80), np.log10(6000), 200)
ax.semilogx(f_sm, mass_law(f_sm, 0.8), 'b-',  lw=2, label='theory σ=0.8')
ax.semilogx(f_sm, mass_law(f_sm, 10),  'r-',  lw=2, label='theory σ=10')
ax.semilogx(f_Hz, TL_cardboard, 'bo', ms=9, label='cardboard measured')
ax.semilogx(f_Hz, TL_gypsum,    'rs', ms=9, label='gypsum measured')
ax.set_xlabel('frequency (Hz)'); ax.set_ylabel('TL (dB)')
ax.set_title('Sound isolation — mass law comparison')
ax.legend(); ax.grid(True, which='both', alpha=0.3)
plt.tight_layout()

# --- بخش ۴: نتایج ---
print("f(Hz)  TL_card_th  meas    TL_gyp_th  meas")
for f, t1, m1, t2, m2 in zip(f_Hz, TL1_th, TL_cardboard, TL2_th, TL_gypsum):
    print(f"{f:5.0f}  {t1:6.1f}    {m1:4.1f}    {t2:6.1f}    {m2:4.1f}")
# slope per octave (should be ~6 dB)
slope1 = np.polyfit(np.log2(f_Hz), TL_cardboard, 1)[0]
slope2 = np.polyfit(np.log2(f_Hz), TL_gypsum, 1)[0]
print(f"ncardboard slope = {slope1:.1f} dB/octave (ideal 6)")
print(f"gypsum    slope = {slope2:.1f} dB/octave (ideal 6)")

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Output

Problem Description & Analysis

Interactive Simulation (Python)

Python Code Lab

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