TS EAMCET · Physics · Waves and Sound
The transverse displacement \(y(x, t)\) of a wave on a string is given by \(y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}\). This represents a
- A wave moving in negative \(x\)-direction with speed \(\sqrt{\frac{b}{a}}\)
- B standing wave of frequency \(\sqrt{b}\)
- C standing wave of frequency \(\frac{1}{\sqrt{b}}\)
- D wave moving in positive \(x\)-direction with speed \(\sqrt{\frac{b}{a}}\)
Answer & Solution
Correct Answer
(A) wave moving in negative \(x\)-direction with speed \(\sqrt{\frac{b}{a}}\)
Step-by-step Solution
Detailed explanation
Phase of given wave is \(\phi=a x^2+b t^2+2 \sqrt{a b} x t\) Differentiating with respect to time, \(\frac{d \phi}{d t}=0=2 a x \frac{d x}{d t}+2 b t+2 \sqrt{a b}\left(t \cdot \frac{d x}{d t}+x\right)\)…
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