expected_frequency = 5.0
matches_expected = np.isclose(dominant_frequency, expected_frequency)

print(f"frequency resolution: {frequencies[1] - frequencies[0]:.1f} Hz")
print(f"dominant frequency: {dominant_frequency:.1f} Hz")
print(f"dominant magnitude: {magnitudes[dominant_index]:.1f}")
print(f"matches expected: {matches_expected}")

if not matches_expected:
    raise RuntimeError("dominant frequency did not match the known signal")