:root {
       
            --accent-color: #1e3799;
            --light-gray: #f8f9fa;
            --border-color: #eaeaea;
            --text-color: #333;
            --text-muted: #6c757d;
            --success-color: #78e08f;
            --warning-color: #fad390;
            --danger-color: #e55039;
            --wave-color: #3498db;
        }
    
        
        .visualization-container {
            height: 400px;
            background-color: var(--light-gray);
            border-radius: 8px;
            border: 1px solid var(--border-color);
            position: relative;
            overflow: hidden;
            margin-top: 2rem;
        }
        
        .wave-canvas {
            width: 100%;
            height: 100%;
        }
        
        .physics-card {
            background-color: rgba(74, 105, 189, 0.1);
            border-left: 4px solid var(--primary-color);
            padding: 1.5rem;
            border-radius: 0 8px 8px 0;
            margin-top: 2rem;
        }
        
        .physics-title {
            font-weight: 600;
            margin-bottom: 1rem;
            color: var(--primary-color);
        }
        
        .formula-card {
            background-color: white;
            border-radius: 8px;
            border: 1px solid var(--border-color);
            padding: 1.5rem;
            margin-top: 1.5rem;
        }
        
        .formula-title {
            font-weight: 600;
            margin-bottom: 1rem;
            color: var(--primary-color);
        }
        
        .formula-content {
            font-family: 'Courier New', monospace;
            background-color: var(--light-gray);
            padding: 1rem;
            border-radius: 6px;
            overflow-x: auto;
            font-size: 1.25rem;
            text-align: center;
        }
        
        .example-card {
            background-color: rgba(120, 224, 143, 0.1);
            border-left: 4px solid var(--success-color);
            padding: 1.5rem;
            border-radius: 0 8px 8px 0;
            margin-top: 2rem;
        }
        
        .example-title {
            font-weight: 600;
            margin-bottom: 1rem;
            color: var(--success-color);
        }
        
        .wave-table {
            width: 100%;
            border-collapse: collapse;
            margin-top: 1.5rem;
        }
        
        .wave-table th, 
        .wave-table td {
            padding: 0.75rem;
            text-align: left;
            border-bottom: 1px solid var(--border-color);
        }
        
        .wave-table th {
            background-color: var(--light-gray);
            font-weight: 600;
        }
        
        .wave-table tr:hover {
            background-color: rgba(74, 105, 189, 0.05);
        }
        
        .wave-animation-container {
            height: 200px;
            background-color: #e9ecef;
            border-radius: 8px;
            position: relative;
            overflow: hidden;
            margin-top: 1.5rem;
        }
        
        .wave-animation {
            position: absolute;
            top: 50%;
            left: 0;
            right: 0;
            height: 100px;
            transform: translateY(-50%);
        }
        
        .wave-path {
            fill: none;
            stroke: var(--wave-color);
            stroke-width: 2;
        }
        
        .wave-point {
            position: absolute;
            width: 12px;
            height: 12px;
            background-color: var(--danger-color);
            border-radius: 50%;
            transform: translate(-50%, -50%);
        }
         
        
        @media (max-width: 768px) {
            .input-row {
                grid-template-columns: 1fr;
                gap: 0.75rem;
            }
            
            .result-grid {
                grid-template-columns: 1fr 1fr;
            }
        }
        
        @media (max-width: 576px) {
            .result-grid {
                grid-template-columns: 1fr;
            }
        }
        
        /* Validation styles */
        .is-invalid {
            border-color: var(--danger-color);
        }
        
        .invalid-feedback {
            display: none;
            width: 100%;
            margin-top: 0.25rem;
            font-size: 0.875em;
            color: var(--danger-color);
        }
        
        .is-invalid ~ .invalid-feedback {
            display: block;
        }