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IBM

MCP Math Server

by IBM

beat_frequency_analysis

Calculate the beat frequency between two interfering waves to analyze interference patterns in wave phenomena.

Instructions

Analyze beat frequency from two interfering waves. (Domain: trigonometry, Category: wave_analysis)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
freq1Yes
freq2Yes
Behavior1/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool does without explaining how it behaves: it doesn't mention what the analysis entails (e.g., calculation method, output format), whether it's a read-only operation, error handling, or any constraints. This leaves critical behavioral traits unspecified, making it inadequate for informed tool selection.

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

Conciseness5/5

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

The description is extremely concise: a single sentence that directly states the tool's purpose, followed by domain and category in parentheses. Every word earns its place with no redundancy or fluff, making it easy to parse and front-loaded with the core functionality. This efficiency is ideal for quick understanding.

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

Completeness2/5

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

Given the complexity (a mathematical analysis tool with two parameters), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It doesn't explain the analysis process, expected results, or any behavioral aspects. While conciseness is high, the tool requires more context for effective use, such as what the output represents or any mathematical assumptions.

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

Parameters2/5

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

The input schema has two parameters (freq1, freq2) with 0% description coverage, meaning the schema provides no semantic information. The description mentions 'two interfering waves' which implies these parameters represent frequencies, but it doesn't specify units (e.g., Hz), valid ranges, or interpretation (e.g., which is primary). This adds minimal meaning beyond the parameter names, insufficient to compensate for the low schema coverage.

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

Purpose4/5

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

The description clearly states the tool's purpose: 'Analyze beat frequency from two interfering waves.' It specifies the verb ('analyze'), resource ('beat frequency'), and context ('from two interfering waves'), making the intent unambiguous. However, it doesn't differentiate from siblings like 'wave_interference' or 'frequency_from_period', which are related but not identical, so it doesn't fully distinguish from alternatives.

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

Usage Guidelines2/5

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

The description provides minimal guidance: it mentions the domain ('trigonometry') and category ('wave_analysis'), which implies a context but doesn't explicitly state when to use this tool versus alternatives like 'wave_interference' or 'frequency_from_period'. There's no mention of prerequisites, exclusions, or specific scenarios, leaving the agent to infer usage based on the name and parameters alone.

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

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