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System default

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Tutoring abilities

If a singer steps slightly to the side of a cardioid microphone, their voice does not just get quieter — it instantly sounds dull, boxy, and hollow.

This tonal change happens because a microphone's pickup shape changes dramatically at different sound frequencies.

A **polar pattern diagram** is a circular graph that plots a microphone's sensitivity in decibels ($	ext{dB}$) across a full $360^\circ$ radius.

The center of the circle represents maximum attenuation (usually $-25\text{ dB}$ or complete silence), while the outer ring represents $0\text{ dB}$ of attenuation — the microphone's maximum sensitivity, usually measured directly in front at **on-axis** ($0^\circ$).

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 10px;
      min-height: 100%;
      user-select: none;
      -webkit-user-select: none;
    }
    .btn-group {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      width: 100%;
      max-width: 360px;
      z-index: 10;
    }
    .btn {
      padding: 6px 12px;
      border: 1px solid #d1d5db;
      background: #ffffff;
      color: #4b5563;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
      transition: background 0.2s, color 0.2s, border-color 0.2s;
    }
    .btn.active {
      background: #22b7ff;
      color: #ffffff;
      border-color: #22b7ff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.35);
    }
    .chart-container {
      position: relative;
      width: 100%;
      max-width: 340px;
      aspect-ratio: 1;
      display: flex;
      align-items: center;
      justify-content: center;
      touch-action: none;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .grid-circle {
      fill: none;
      stroke: #e5e7eb;
      stroke-width: 1.2;
    }
    .grid-line {
      stroke: #e5e7eb;
      stroke-width: 1.2;
      stroke-dasharray: 3 3;
    }
    .axis-label {
      font-size: 11px;
      font-weight: 700;
      fill: #6b7280;
      text-anchor: middle;
      dominant-baseline: central;
    }
    .db-label {
      font-size: 9px;
      font-weight: 600;
      fill: #9ca3af;
      text-anchor: middle;
    }
    .polar-curve {
      fill: rgba(34, 183, 255, 0.15);
      stroke: #0284c7;
      stroke-width: 2.5;
      stroke-linejoin: round;
      transition: d 0.35s ease;
    }
    .probe-line {
      stroke: #f59e0b;
      stroke-width: 1.8;
      stroke-dasharray: 4 2;
    }
    .source-handle {
      cursor: grab;
    }
    .status-bar {
      display: flex;
      align-items: center;
      justify-content: space-around;
      width: 100%;
      max-width: 340px;
      background: #ffffff;
      border: 1px solid #e5e7eb;
      border-radius: 12px;
      padding: 8px 14px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
      font-size: 13px;
      font-weight: 600;
    }
    .meter-wrap {
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .meter-bar-bg {
      width: 60px;
      height: 8px;
      background: #e5e7eb;
      border-radius: 4px;
      overflow: hidden;
    }
    .meter-bar-fill {
      height: 100%;
      background: #22b7ff;
      border-radius: 4px;
      transition: width 0.1s ease, background-color 0.2s ease;
    }
  </style>
</head>
<body>

  <div class="btn-group" id="patternBtns">
    <button class="btn active" data-pattern="cardioid">Cardioid</button>
    <button class="btn" data-pattern="omni">Omni</button>
    <button class="btn" data-pattern="figure8">Figure-8</button>
    <button class="btn" data-pattern="supercardioid">Supercardioid</button>
  </div>

  <div class="chart-container" id="chartArea">
    <svg viewBox="0 0 300 300" id="polarSvg">
      
      <circle class="grid-circle" cx="150" cy="150" r="120" stroke="#cbd5e1" stroke-width="1.5" />
      <circle class="grid-circle" cx="150" cy="150" r="96" />
      <circle class="grid-circle" cx="150" cy="150" r="72" />
      <circle class="grid-circle" cx="150" cy="150" r="48" />
      <circle class="grid-circle" cx="150" cy="150" r="24" />

      
      <line class="grid-line" x1="150" y1="30" x2="150" y2="270" />
      <line class="grid-line" x1="30" y1="150" x2="270" y2="150" />
      <line class="grid-line" x1="65" y1="65" x2="235" y2="235" />
      <line class="grid-line" x1="65" y1="235" x2="235" y2="65" />

      
      <text class="db-label" x="150" y="27">0 dB</text>
      <text class="db-label" x="150" y="51">-5 dB</text>
      <text class="db-label" x="150" y="75">-10 dB</text>
      <text class="db-label" x="150" y="99">-15 dB</text>
      <text class="db-label" x="150" y="123">-20 dB</text>

      
      <text class="axis-label" x="150" y="14">0°</text>
      <text class="axis-label" x="286" y="150">90°</text>
      <text class="axis-label" x="150" y="286">180°</text>
      <text class="axis-label" x="14" y="150">270°</text>

      
      <path class="polar-curve" id="curvePath" d="" />

      
      <line class="probe-line" id="probeLine" x1="150" y1="150" x2="150" y2="30" />

      
      <circle id="responsePoint" cx="150" cy="30" r="4.5" fill="#0284c7" stroke="#ffffff" stroke-width="1.5" />

      
      <g transform="translate(150, 150)">
        <circle cx="0" cy="0" r="13" fill="#ffffff" stroke="#94a3b8" stroke-width="1.5" />
        <text text-anchor="middle" dominant-baseline="central" font-size="14" y="1">🎙</text>
      </g>

      
      <g id="sourceHandle" class="source-handle" transform="translate(150, 30)">
        <circle cx="0" cy="0" r="14" fill="#f59e0b" filter="drop-shadow(0 2px 4px rgba(0,0,0,0.15))" />
        <text text-anchor="middle" dominant-baseline="central" font-size="12" y="1">🔊</text>
      </g>
    </svg>
  </div>

  <div class="status-bar">
    <div>Angle: <span id="angleText" style="color:#f59e0b">0°</span></div>
    <div class="meter-wrap">
      <span>Level:</span>
      <div class="meter-bar-bg">
        <div class="meter-bar-fill" id="meterFill" style="width: 100%;"></div>
      </div>
      <span id="dbText" style="color:#0284c7; min-width: 48px;">0.0 dB</span>
    </div>
  </div>

  <script>
    const R_MAX = 120;
    const CENTER = 150;
    const DB_MIN = -25;

    let currentPattern = 'cardioid';
    let currentAngleDeg = 0;
    let isDragging = false;

    function getGain(pattern, rad) {
      switch (pattern) {
        case 'omni':
          return 1.0;
        case 'figure8':
          return Math.abs(Math.cos(rad));
        case 'supercardioid':
          return Math.abs(0.37 + 0.63 * Math.cos(rad));
        case 'cardioid':
        default:
          return 0.5 + 0.5 * Math.cos(rad);
      }
    }

    function gainToRadius(gain) {
      const db = gain <= 0.0001 ? DB_MIN : Math.max(DB_MIN, 20 * Math.log10(gain));
      const normalized = (db - DB_MIN) / (0 - DB_MIN); // 0 to 1
      return Math.max(0, normalized * R_MAX);
    }

    function buildCurvePath(pattern) {
      const steps = 120;
      let d = '';
      for (let i = 0; i <= steps; i++) {
        const theta = (i / steps) * 2 * Math.PI; // 0 at 0° (top)
        const gain = getGain(pattern, theta);
        const r = gainToRadius(gain);
        // theta=0 is at top (-Y in SVG)
        const x = CENTER + r * Math.sin(theta);
        const y = CENTER - r * Math.cos(theta);
        d += (i === 0 ? 'M ' : 'L ') + x.toFixed(1) + ' ' + y.toFixed(1);
      }
      return d + ' Z';
    }

    function update() {
      // Update curve
      document.getElementById('curvePath').setAttribute('d', buildCurvePath(currentPattern));

      // Calculate current angle in radians
      const rad = (currentAngleDeg * Math.PI) / 180;
      const gain = getGain(currentPattern, rad);
      const rResp = gainToRadius(gain);

      // Sound source position (on outer ring)
      const srcX = CENTER + R_MAX * Math.sin(rad);
      const srcY = CENTER - R_MAX * Math.cos(rad);
      document.getElementById('sourceHandle').setAttribute('transform', `translate(${srcX.toFixed(1)}, ${srcY.toFixed(1)})`);

      // Probe line
      const probeLine = document.getElementById('probeLine');
      probeLine.setAttribute('x2', srcX.toFixed(1));
      probeLine.setAttribute('y2', srcY.toFixed(1));

      // Response point
      const respX = CENTER + rResp * Math.sin(rad);
      const respY = CENTER - rResp * Math.cos(rad);
      const respDot = document.getElementById('responsePoint');
      respDot.setAttribute('cx', respX.toFixed(1));
      respDot.setAttribute('cy', respY.toFixed(1));

      // Readouts
      const db = gain <= 0.0001 ? -25 : Math.max(-25, 20 * Math.log10(gain));
      document.getElementById('angleText').textContent = `${Math.round(currentAngleDeg)}°`;
      document.getElementById('dbText').textContent = db <= -24.9 ? '-∞ dB' : `${db.toFixed(1)} dB`;

      // Level bar
      const fillPct = Math.max(0, Math.min(100, ((db - DB_MIN) / (0 - DB_MIN)) * 100));
      const meterFill = document.getElementById('meterFill');
      meterFill.style.width = `${fillPct}%`;
      meterFill.style.backgroundColor = fillPct > 60 ? '#22b7ff' : (fillPct > 25 ? '#f59e0b' : '#9ca3af');
    }

    // Pattern switcher
    const btns = document.querySelectorAll('#patternBtns .btn');
    btns.forEach(btn => {
      btn.addEventListener('click', () => {
        btns.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        currentPattern = btn.getAttribute('data-pattern');
        update();
      });
    });

    // Pointer/Touch interaction to rotate probe
    const chartArea = document.getElementById('chartArea');
    const svg = document.getElementById('polarSvg');

    function setAngleFromPointer(e) {
      const rect = svg.getBoundingClientRect();
      const clientX = e.touches ? e.touches[0].clientX : e.clientX;
      const clientY = e.touches ? e.touches[0].clientY : e.clientY;
      const cx = rect.left + rect.width / 2;
      const cy = rect.top + rect.height / 2;
      const dx = clientX - cx;
      const dy = clientY - cy;

      // Angle from top (0 deg)
      let deg = (Math.atan2(dx, -dy) * 180) / Math.PI;
      if (deg < 0) deg += 360;
      currentAngleDeg = deg;
      update();
    }

    chartArea.addEventListener('pointerdown', (e) => {
      isDragging = true;
      setAngleFromPointer(e);
    });

    window.addEventListener('pointermove', (e) => {
      if (isDragging) setAngleFromPointer(e);
    });

    window.addEventListener('pointerup', () => {
      isDragging = false;
    });

    window.addEventListener('pointercancel', () => {
      isDragging = false;
    });

    // Initial render
    update();
  </script>
</body>
</html>

Why do polar charts show multiple nested lines instead of just one clean curve?

Sound directivity depends on **wavelength** ($\lambda$), calculated as $\lambda = v / f$, where $v$ is the speed of sound ($343\text{ m/s}$) and $f$ is frequency.

Long low-frequency waves (like $100\text{ Hz}$ at $3.4\text{ meters}$) easily bend around a microphone capsule via **diffraction**, making the microphone respond nearly omnidirectionally in the bass range.

Short high-frequency waves (like $10\text{ kHz}$ at $3.4\text{ cm}$) cannot wrap around the microphone body, causing the pickup pattern to **beam** and narrow significantly at the front.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
      -webkit-user-select: none;
    }

    .main-stage {
      position: relative;
      width: 100%;
      max-width: 360px;
      aspect-ratio: 1 / 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .legend-row {
      display: flex;
      justify-content: center;
      gap: 12px;
      font-size: 12px;
      font-weight: 600;
      margin-bottom: 4px;
    }
    .legend-item {
      display: flex;
      align-items: center;
      gap: 5px;
    }
    .dot-key {
      width: 10px;
      height: 10px;
      border-radius: 50%;
    }

    .controls-panel {
      width: 100%;
      max-width: 360px;
      background: #ffffff;
      border-radius: 12px;
      padding: 10px 14px;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .slider-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 10px;
      font-size: 13px;
      font-weight: 600;
    }

    input[type="range"] {
      flex: 1;
      accent-color: #22b7ff;
      cursor: pointer;
      height: 6px;
    }

    .spectrum-row {
      display: flex;
      align-items: flex-end;
      justify-content: space-around;
      height: 42px;
      padding: 4px 8px 0;
      background: #f1f5f9;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
    }

    .bar-group {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 3px;
      width: 28%;
      height: 100%;
      justify-content: flex-end;
    }

    .bar-track {
      width: 100%;
      height: 22px;
      background: #e2e8f0;
      border-radius: 3px;
      position: relative;
      overflow: hidden;
      display: flex;
      align-items: flex-end;
    }

    .bar-fill {
      width: 100%;
      border-radius: 3px;
      transition: height 0.2s ease;
    }

    .bar-label {
      font-size: 10px;
      font-weight: 700;
      color: #64748b;
    }

    .audio-btn {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      background: #22b7ff;
      color: #fff;
      border: none;
      border-radius: 8px;
      padding: 6px 12px;
      font-size: 12px;
      font-weight: 700;
      cursor: pointer;
      box-shadow: 0 2px 4px rgba(34, 183, 255, 0.25);
    }
    .audio-btn:active {
      opacity: 0.9;
    }
  </style>
</head>
<body>

  <div class="legend-row">
    <div class="legend-item">
      <span class="dot-key" style="background:#3b82f6;"></span>
      <span>250 Hz (Wide)</span>
    </div>
    <div class="legend-item">
      <span class="dot-key" style="background:#10b981;"></span>
      <span>1 kHz (Cardioid)</span>
    </div>
    <div class="legend-item">
      <span class="dot-key" style="background:#ef4444;"></span>
      <span>10 kHz (Beaming)</span>
    </div>
  </div>

  <div class="main-stage">
    <svg viewBox="-140 -140 280 280">
      
      <circle cx="0" cy="0" r="30" fill="none" stroke="#e2e8f0" stroke-dasharray="3,3" />
      <circle cx="0" cy="0" r="60" fill="none" stroke="#e2e8f0" stroke-dasharray="3,3" />
      <circle cx="0" cy="0" r="90" fill="none" stroke="#cbd5e1" stroke-width="1" />
      <circle cx="0" cy="0" r="115" fill="none" stroke="#e2e8f0" stroke-width="0.5" />

      
      <line x1="0" y1="-120" x2="0" y2="120" stroke="#cbd5e1" stroke-width="1" />
      <line x1="-120" y1="0" x2="120" y2="0" stroke="#cbd5e1" stroke-width="1" />

      
      <text x="0" y="-123" text-anchor="middle" font-size="10" font-weight="700" fill="#64748b">0° (On-Axis)</text>
      <text x="125" y="4" text-anchor="start" font-size="10" font-weight="700" fill="#64748b">90°</text>
      <text x="0" y="132" text-anchor="middle" font-size="10" font-weight="700" fill="#64748b">180°</text>

      
      
      <path id="curve-low" fill="none" stroke="#3b82f6" stroke-width="2" opacity="0.85" />

      
      <path id="curve-mid" fill="none" stroke="#10b981" stroke-width="2.5" />

      
      <path id="curve-high" fill="none" stroke="#ef4444" stroke-width="2.5" stroke-dasharray="4,2" />

      
      <g transform="translate(0, 0)">
        <rect x="-6" y="-12" width="12" height="24" rx="6" fill="#1e2945" />
        <line x1="-6" y1="-4" x2="6" y2="-4" stroke="#94a3b8" stroke-width="1" />
        <line x1="-6" y1="0" x2="6" y2="0" stroke="#94a3b8" stroke-width="1" />
        <circle cx="0" cy="-12" r="3" fill="#ef4444" />
      </g>

      
      <line id="source-ray" x1="0" y1="0" x2="0" y2="-105" stroke="#f59e0b" stroke-width="2" stroke-dasharray="3,3" />
      <g id="source-group" transform="translate(0, -105)">
        <circle r="14" fill="#fef3c7" stroke="#f59e0b" stroke-width="2" />
        <text y="4" text-anchor="middle" font-size="12">🔊</text>
      </g>
    </svg>
  </div>

  <div class="controls-panel">
    <div class="slider-row">
      <span>Angle: <strong id="angle-text">0°</strong></span>
      <input type="range" id="angle-slider" min="0" max="90" value="0" step="1">
      <button class="audio-btn" id="audio-btn">Preview 🎵</button>
    </div>

    
    <div class="spectrum-row">
      <div class="bar-group">
        <div class="bar-track">
          <div class="bar-fill" id="bar-low" style="background:#3b82f6; height:100%;"></div>
        </div>
        <span class="bar-label">LOW</span>
      </div>
      <div class="bar-group">
        <div class="bar-track">
          <div class="bar-fill" id="bar-mid" style="background:#10b981; height:100%;"></div>
        </div>
        <span class="bar-label">MID</span>
      </div>
      <div class="bar-group">
        <div class="bar-track">
          <div class="bar-fill" id="bar-high" style="background:#ef4444; height:100%;"></div>
        </div>
        <span class="bar-label">HIGH</span>
      </div>
    </div>
  </div>

  <script>
    // Generate Polar Curves
    const maxR = 90;

    function polarToCartesian(rNorm, deg) {
      const rad = (deg - 90) * (Math.PI / 180);
      const r = rNorm * maxR;
      return { x: r * Math.cos(rad), y: r * Math.sin(rad) };
    }

    function buildPath(fn) {
      let d = '';
      for (let i = 0; i <= 360; i += 2) {
        const rNorm = Math.max(0, fn(i * Math.PI / 180));
        const pt = polarToCartesian(rNorm, i);
        d += (i === 0 ? 'M' : 'L') + ` ${pt.x.toFixed(1)} ${pt.y.toFixed(1)} `;
      }
      return d + 'Z';
    }

    // Low: 0.65 + 0.35*cos(th)
    document.getElementById('curve-low').setAttribute('d', buildPath(th => 0.68 + 0.32 * Math.cos(th)));

    // Mid (Cardioid): 0.5 + 0.5*cos(th)
    document.getElementById('curve-mid').setAttribute('d', buildPath(th => 0.5 + 0.5 * Math.cos(th)));

    // High (10 kHz Beaming): sharp drop-off off-axis
    document.getElementById('curve-high').setAttribute('d', buildPath(th => {
      const cosVal = Math.cos(th);
      if (cosVal <= 0) return 0.05;
      return Math.pow(cosVal, 2.5);
    }));

    // Interactive Slider & Live Responses
    const slider = document.getElementById('angle-slider');
    const angleText = document.getElementById('angle-text');
    const sourceGroup = document.getElementById('source-group');
    const sourceRay = document.getElementById('source-ray');
    const barLow = document.getElementById('bar-low');
    const barMid = document.getElementById('bar-mid');
    const barHigh = document.getElementById('bar-high');

    function updateAngle(deg) {
      angleText.textContent = `${deg}°` + (deg === 0 ? ' (On-Axis)' : deg === 90 ? ' (Off-Axis)' : '');

      const rad = deg * (Math.PI / 180);
      const rayPt = polarToCartesian(1.15, deg);

      sourceGroup.setAttribute('transform', `translate(${rayPt.x.toFixed(1)}, ${rayPt.y.toFixed(1)})`);
      sourceRay.setAttribute('x2', rayPt.x.toFixed(1));
      sourceRay.setAttribute('y2', rayPt.y.toFixed(1));

      // Frequency Response Calculations at given angle
      const lowGain = Math.max(0.1, 0.68 + 0.32 * Math.cos(rad));
      const midGain = Math.max(0.1, 0.5 + 0.5 * Math.cos(rad));
      const highGain = Math.max(0.04, Math.cos(rad) > 0 ? Math.pow(Math.cos(rad), 2.5) : 0.04);

      barLow.style.height = `${(lowGain * 100).toFixed(0)}%`;
      barMid.style.height = `${(midGain * 100).toFixed(0)}%`;
      barHigh.style.height = `${(highGain * 100).toFixed(0)}%`;

      if (filterNode) {
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        const cutoff = 800 + (12000 - 800) * highGain;
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    slider.addEventListener('input', (e) => updateAngle(parseInt(e.target.value)));

    // Web Audio Tone Synthesis for Off-Axis Colouration Preview
    let audioCtx = null;
    let filterNode = null;
    let isPlaying = false;

    document.getElementById('audio-btn').addEventListener('click', () => {
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      if (audioCtx.state === 'suspended') {
        audioCtx.resume();
      }

      if (isPlaying) return;
      isPlaying = true;

      const deg = parseInt(slider.value);
      const rad = deg * (Math.PI / 180);
      const highGain = Math.max(0.04, Math.cos(rad) > 0 ? Math.pow(Math.cos(rad), 2.5) : 0.04);

      // Create pink/rich harmonic burst (fundamental + harmonics to hear HF loss clearly)
      const now = audioCtx.currentTime;
      filterNode = audioCtx.createBiquadFilter();
      filterNode.type = 'lowpass';
      filterNode.frequency.value = 800 + (12000 - 800) * highGain;
      filterNode.Q.value = 1.0;

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      masterGain.gain.setValueAtTime(0.2, now);
      masterGain.gain.exponentialRampToValueAtTime(0.001, now + 1.2);

      filterNode.connect(masterGain);
      masterGain.connect(audioCtx.destination);

      // Multi-oscillator bright chord
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      freqs.forEach(f => {
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        osc.connect(filterNode);
        osc.start(now);
        osc.stop(now + 1.2);
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      setTimeout(() => { isPlaying = false; }, 1250);
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    updateAngle(0);
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When high frequencies are rejected far more aggressively than low frequencies off to the side, what happens to the captured sound?

**Off-axis colouration** occurs when a microphone alters the frequency response of sound arriving from an angle, changing its tonal character.

Because directional microphones attenuate high frequencies much more than lows at $60^\circ$ to $90^\circ$ off-axis, off-axis sources (such as cymbals bleeding into a snare mic) sound dark, muddy, and unnatural.

Directional capsules use rear acoustic vents to create an internal time delay: waves entering from the rear reach both sides of the diaphragm at the same time and cancel out.

When off-axis sound enters these vents at intermediate angles ($45^\circ$ to $135^\circ$), imperfect acoustic cancellation creates **phase smearing** and comb-filtering notches across the treble spectrum.

Diaphragm size also intensifies this problem, especially in a **Large Diaphragm Condenser (LDC)**.

When complex, high-frequency transients arrive off-axis, the wavefront reaches one edge of the wide diaphragm surface slightly before the opposite edge.

This time delay across the physical capsule causes direct **phase cancellation** across different points on the diaphragm surface, resulting in noticeable **phase smearing** and **comb filtering**.

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  <div class="toolbar">
    <button class="btn-chip active" onclick="setPattern('cardioid')">Cardioid</button>
    <button class="btn-chip" onclick="setPattern('figure8')">Figure-8</button>
    <button class="btn-chip" onclick="setPattern('omni')">Omni</button>
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  <div class="workspace">
    
    <div class="panel-card">
      <div class="panel-title">Polar Pattern</div>
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        <rect x="-4" y="-10" width="8" height="20" rx="4" fill="#1e2945" />
        <circle cx="0" cy="-6" r="3" fill="#22b7ff" />

        
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          <circle cx="0" cy="-82" r="6" fill="#ef4444" />
          <text cx="0" cy="-82" text-anchor="middle" font-size="10" y="-87" fill="#ef4444" font-weight="700">🔊</text>
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    <div class="panel-card">
      <div class="panel-title">Frequency Response</div>
      <svg id="freqSvg" viewBox="0 0 200 160">
        
        <line x1="25" y1="20" x2="25" y2="135" stroke="#9ca3af" stroke-width="1" />
        <line x1="25" y1="135" x2="190" y2="135" stroke="#9ca3af" stroke-width="1" />
        
        
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Diaphragm size also amplifies this issue. In a **Large Diaphragm Condenser (LDC)**, the physical membrane (typically $1\text{ inch}$ / $25\text{ mm}$ across) is wider than the wavelengths of high-frequency transients.

When complex, high-frequency sound waves arrive off-axis, the wavefront hits the closer edge of the diaphragm slightly before the farther edge.

This time delay across different points of the diaphragm surface triggers acoustic **phase cancellation**, causing severe off-axis phase smearing and comb filtering.

How do sound engineers apply this knowledge to solve spill problems during live recordings?

Suppose you are miking a snare drum with a cardioid dynamic microphone, and a loud hi-hat sits $90^\circ$ to the side.

According to the microphone's polar plot, the sensitivity at $90^\circ$ is $-6\text{ dB}$ at $500\text{ Hz}$, but $-18\text{ dB}$ at $8\text{ kHz}$.

The hi-hat spill does not simply disappear; its high-end sizzle is cut by $18\text{ dB}$ while its midrange clatter is only cut by $6\text{ dB}$, turning the bleed into a boxy 'trash-can' resonance.

A common mistake in studio setups is pointing the rear ($180^\circ$) of a hypercardioid or supercardioid mic directly at an unwanted source like a floor monitor, forgetting that these patterns have a rear pickup lobe that introduces severe off-axis treble bleed.

When choosing and aiming microphones in a live room, always check the frequency curves on the polar chart to ensure the angle of spill falls on the truest null point.

music-technology

Interpreting Microphone Polar Pattern Diagrams and Off-Axis Colouration. Analyse how frequency-dependent narrowing of polar patterns causes high-frequency off-axis phase smearing and spectral colouration.

Choosing & Using Microphone Polar Patterns

Directional vs Omnidirectional Microphones and Polar Pattern Behavior

Microphone Basics: Transducers, Polar Patterns, & Frequency Response

To master MUSTECH-5.4 at A2 Level, instruction should connect polar diagrams to physical acoustics. Begin with critical listening tests comparing identical sources recorded on-axis vs $90^\circ$ off-axis using both small-diaphragm and large-diaphragm cardioid microphones. Next, guide students to interpret multi-frequency polar charts by tracing how the pattern narrows as frequency increases from $125\text{ Hz}$ to $16\text{ kHz}$. Finally, have students perform mathematical calculations comparing acoustic wavelength $\lambda = \frac{c}{f}$ to diaphragm diameter $d$ to reinforce the physical causes of acoustic shadowing, phase cancellation, and off-axis colouration.

Interpreting Microphone Polar Pattern Diagrams and Off-Axis Colouration

Reading a Polar Plot

Frequency-Dependent Narrowing