Problem 6 IYPT 2027: 6. Seeing sound

Problem Description & Analysis

A thin rubber membrane is stretched over a circular frame and driven into vibration by a loudspeaker. A small mirror is attached to the membrane, and a laser beam is reflected off it onto a distant screen. Under certain conditions, the laser spot traces out complex, steady, or evolving geometric patterns. Investigate the relationship between the driving parameters, the membrane’s properties, and the resulting light patterns.

Interactive Simulation (Python)

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فرکانس صوت (Hz) 1000 Hz

سرعت صوت v (m/s) 343 m/s

طول لولهٔ کوندت L (m) 1 m

دامنهٔ نسبی 1

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Python Code Lab

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Python — Editable

# آزمایش «دیدن صدا» — اندازه‌گیری فاصلهٔ گره‌ها در لولهٔ کوندت
import numpy as np
import matplotlib.pyplot as plt

# --- بخش ۱: داده‌های شما ---
# در چند فرکانس، فاصلهٔ متوسط بین گره‌های پودر (cm) را اندازه گرفتید
f_Hz     = np.array([500,  800, 1000, 1500, 2000, 3000])
d_node_cm = np.array([34.1, 21.4, 17.2, 11.5, 8.7,  5.8])

# --- بخش ۲: نظریه: d_node = λ/2 = v/(2f)  →  v = 2 f d_node
v_meas = 2 * f_Hz * (d_node_cm/100)   # m/s
v_avg  = np.mean(v_meas)

# --- بخش ۳: نمودار ---
fig, ax = plt.subplots(1, 2, figsize=(11, 4.5))
f_smooth = np.linspace(f_Hz.min()*0.9, f_Hz.max()*1.1, 200)
d_theory = 343.0/(2*f_smooth) * 100
ax[0].plot(f_smooth, d_theory, 'b-', lw=2, label='d = v/(2f), v=343 m/s')
ax[0].plot(f_Hz, d_node_cm, 'ro', ms=9, label='measured')
ax[0].set_xlabel('frequency (Hz)'); ax[0].set_ylabel('node spacing (cm)')
ax[0].set_title('Node spacing vs frequency')
ax[0].legend(); ax[0].grid(True, alpha=0.3)

ax[1].plot(f_Hz, v_meas, 'go', ms=9)
ax[1].axhline(v_avg, color='b', ls='--', label=f'mean = {v_avg:.1f} m/s')
ax[1].axhline(343, color='r', ls=':', label='literature 343 m/s')
ax[1].set_xlabel('frequency (Hz)'); ax[1].set_ylabel('inferred sound speed (m/s)')
ax[1].set_title('Sound speed from d_node·2·f')
ax[1].legend(); ax[1].grid(True, alpha=0.3)

plt.tight_layout()

# --- بخش ۴: نتایج ---
print(" f(Hz)  d_node(cm)  v_inferred(m/s)")
for f, d, v in zip(f_Hz, d_node_cm, v_meas):
    print(f" {f:5.0f}    {d:6.2f}       {v:6.1f}")
print(f"nMean inferred sound speed = {v_avg:.1f} m/s (literature ≈ 343 m/s at 20°C)")
print(f"Deviation from 343 m/s    = {(v_avg-343)/343*100:+.2f}%")

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Output

Problem Description & Analysis

Interactive Simulation (Python)

Python Code Lab

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