Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint/idempotentHint/non-destructive, so safety needs no restatement. The description adds the governing formula and notes it returns the missing value, which is modest added context (and partly redundant since an output schema exists). It discloses no defaults or resolution behavior beyond 'Returns missing values'.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Compact and front-loaded: verb, formula, domain, inputs, output, cross-reference. Every element is short, though the 'any 2 of...' clause is wasted space because it misdescribes the schema and the trailing list_bundles pointer dilutes the focus.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

An output schema and full annotation set cover the safety and return contracts, so those needn't be explained. But the description's core input contract is inconsistent with the schema (nonexistent wavelength param, 'any 2' vs a required frequency), leaving an agent unsure what the tool actually computes — a material completeness failure for a parameterized calculator.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100% and the schema documents frequency_hz and speed_ms (with the 343 sound default). The description actively introduces a 'wavelength m' input and a 'pick any 2' contract that the schema does not support (frequency_hz is required, and no wavelength field exists), which confuses rather than clarifies parameter semantics.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific verb ('Compute') and resources (wave frequency, wavelength, or period) with a formula, which is clear on its face. However, it does not differentiate from the very close sibling calculate_wavelength_frequency (nor calculate_speed_of_sound), and its stated scope ('any two of frequency/wavelength/speed') does not match the tool's actual capabilities, making the purpose partly misleading.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

'Use for physics or acoustics' is a vague domain hint rather than a when-to-use/when-not-to-use rule. It offers a cross-reference to list_bundles for 'science' calculators but never routes the agent to or away from the directly competing siblings like calculate_wavelength_frequency or calculate_pendulum_period.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.