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### संख्यात्मक समाधान #### (1) तरंग के गुणांक: दी गई तरंग समीकरण है: \[ y(x, t) = 3.0 \sin(3.52t - 2.01x) \, \text{cm} \] इस समीकरण में: - \( y(x, t) \) : विस्थापन (displacement) - \( t \) : समय (time) - \( x \) : स्थान (position) - \( 3.0 \) : आयाम (amplitude) cm - \( 3.52 \) : समय-आवृत्ति (angular frequency, \( \omega \)) rad/s - \( 2.01 \) : स्थान-आवृत्ति (wave number, \( k \)) rad/cm हम इन गुणांक से विभिन्न तरंगीय गुणों की गणना करेंगे। ##### आयाम: आयाम \( A = 3.0 \, \text{cm} \). ##### तरंग संख्या \( k \) (Wave Number): तरंग संख्या \( k \) का सूत्र है: \[ k = 2\pi / \lambda \] जहां \( \lambda \) तरंगदैर्घ्य (wavelength) है। समीकरण में \( k = 2.01 \, \text{rad/cm} \), तो \[ \lambda = \frac{2\pi}{k} = \frac{2\pi}{2.01} \approx 3.13 \, \text{cm} \] ##### आवृत्ति \( f \) (Frequency): आवृत्ति \( f \) का सूत्र है: \[ f = \frac{\omega}{2\pi} \] ___ ____ ____ __________ ___ ____ ___ _________ ________ _____ ___ _________.
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