SOR
145 lines
5.4 KiB
Python
145 lines
5.4 KiB
Python
import math
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from decimal import Decimal
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"""
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Speed of Sound Calculator (Successive Difference Method)
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声速测量计算器 (逐差法)
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参考了 Newton's rings.py 的高精度与不确定度修约逻辑。
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计算公式说明:
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1. 理论声速公式:
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v_t = 331.45 * sqrt(1 + t / 273.15)
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其中 t 为摄氏温度。
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2. 逐差法计算波长 λ:
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本实验两组数据均为 12 个点，分成两组进行逐差：Δx_i = x_{i+6} - x_i (i=1..6)
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- 干涉法 (驻波法) 找振幅最大处：相邻两次最大处间距为 λ/2
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因此 Δx = 6 * (λ/2) = 3λ => λ = Δx_avg / 3
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- 相位法 (李萨如图像) 变为相同方向直线：相邻两次相位改变 2π，间距为 λ
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因此 Δx = 6 * λ => λ = Δx_avg / 6
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3. 声速公式:
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v = f * λ
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4. 不确定度传递公式:
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- Δx_avg 的 A 类不确定度: u_A(Δx_avg) = S_Δ / sqrt(M) (其中 S_Δ 为逐差后 Δx 的标准差, M=6)
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- 坐标 x 的 B 类不确定度: u_B(x) = Δ_inst / sqrt(3) (假设均匀分布)
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- 逐差平均值的 B 类不确定度传播: u_B(Δx_avg) = sqrt(2/M) * u_B(x)
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- Δx_avg 的合成不确定度: u_c(Δx_avg) = sqrt(u_A^2 + u_B^2)
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- 波长 λ 的不确定度:
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干涉法 u(λ) = u_c(Δx_avg) / 3
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相位法 u(λ) = u_c(Δx_avg) / 6
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- 声速 v 的不确定度 (忽略 f 的极小不确定度): u(v) = f * u(λ)
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"""
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from utils import scientific_round
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def calculate_method(method_name, f, k, delta_inst):
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print(f"\n========================================")
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print(f" {method_name} ")
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print(f"========================================")
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print("请输入12个坐标数据 (单位: mm)。")
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x_vals = []
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for i in range(1, 13):
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while True:
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try:
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val_str = input(f"x_{i:02d} = ").strip()
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if not val_str:
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continue
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x_vals.append(Decimal(val_str))
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break
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except Exception:
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print("无效输入！请输入正确的数值。")
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# 1. 逐差计算
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M = 6
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deltas = []
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print("\n--- 逐差过程 ---")
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for i in range(M):
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diff = x_vals[i + M] - x_vals[i]
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deltas.append(diff)
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print(f"Δx_{i+1} = x_{i+M+1} - x_{i+1} = {x_vals[i+M]} - {x_vals[i]} = {diff} mm")
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mean_delta = sum(deltas) / Decimal(str(M))
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# 2. 波长与声速计算
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# 将毫米转换为米计算速度
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wavelength_mm = mean_delta / Decimal(str(k))
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wavelength_m = wavelength_mm / Decimal("1000")
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velocity = Decimal(str(f)) * wavelength_m
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# 3. 不确定度计算
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# u_A
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variance_delta = sum((d - mean_delta)**2 for d in deltas) / Decimal(str(M - 1))
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s_delta = Decimal(str(math.sqrt(float(variance_delta))))
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u_a_delta = s_delta / Decimal(str(math.sqrt(M)))
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# u_B
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u_x = delta_inst / Decimal(str(math.sqrt(3)))
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u_b_delta = Decimal(str(math.sqrt(2.0 / M))) * u_x
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# u_c(Δx_avg)
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u_delta_combined = Decimal(str(math.sqrt(float(u_a_delta**2 + u_b_delta**2))))
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# 传播到波长和声速
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u_wavelength_mm = u_delta_combined / Decimal(str(k))
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u_wavelength_m = u_wavelength_mm / Decimal("1000")
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u_velocity = Decimal(str(f)) * u_wavelength_m
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# 4. 修约与展示
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v_final, uv_final = scientific_round(velocity, u_velocity)
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print("\n--- 中间统计结果 (高精度) ---")
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print(f"平均差值 Δx_avg: {mean_delta:.6f} mm")
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print(f"Δx 的标准差 S_Δ: {s_delta:.6f} mm")
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print(f"Δx_avg 的 A 类不确定度 u_A: {u_a_delta:.6f} mm")
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print(f"Δx_avg 的 B 类不确定度 u_B: {u_b_delta:.6f} mm")
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print(f"波长 λ: {wavelength_mm:.6f} mm")
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print(f"波长的不确定度 u(λ): {u_wavelength_mm:.6f} mm")
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print("\n========================================")
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print(f" {method_name} 最终结果 (四舍六入五凑偶)")
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print(f" v = {v_final} ± {uv_final} m/s")
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print("========================================")
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def main():
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print("========================================")
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print(" 声速测量计算器 ")
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print("========================================")
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t_input = input("请输入环境温度 t (℃) [默认 24]: ").strip() or "24"
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f_input = input("请输入谐振波频率 f (Hz) [默认 37000]: ").strip() or "37000"
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delta_inst_input = input("请输入游标卡尺/测微鼓轮分度值误差 Δ_inst (mm) [默认 0.02]: ").strip() or "0.02"
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t = float(t_input)
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f = float(f_input)
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delta_inst = Decimal(delta_inst_input)
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# 计算理论声速
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v_t = 331.45 * math.sqrt(1 + t / 273.15)
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print(f"\n理论声速 v_t = {v_t:.2f} m/s (温度 {t} ℃)")
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while True:
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print("\n请选择计算方法:")
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print("1. 干涉法 (驻波法) - 振幅最大处")
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print("2. 相位法 (李萨如法) - 相同方向直线")
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print("3. 退出")
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choice = input("请输入选项 (1/2/3): ").strip()
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if choice == '1':
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# 干涉法 k = 3 (Δx_avg = 3λ)
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calculate_method("干涉法 (振幅最大处)", f, 3, delta_inst)
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elif choice == '2':
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# 相位法 k = 6 (Δx_avg = 6λ)
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calculate_method("相位法 (相同方向直线)", f, 6, delta_inst)
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elif choice == '3':
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print("退出程序。")
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break
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else:
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print("无效选项，请重新输入。")
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if __name__ == "__main__":
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main()
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