Equation of a stationary and a travelling waves are as follows y1=Asinkxcosωt and y2=Asin(ωt−kx). The phase difference between two points x1=π3k and x2=3π2k is ϕ1 for the standing wave and ϕ2 for the travelling wave. If the ratio ϕ1ϕ2=3a7b then ab=

For the stationary wave, y1=asin⁡kxcos⁡ωtx1=π3k=λ6 λ2 ϕ1=πFor the travelling wave, ϕ2=k×Δx=7π6⇒ϕ1ϕ2=67

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Equation of a stationary and a travelling waves are as follows $y_{1} = A \sin k x \cos ω t$ and $y_{2} = A \sin (ω t - k x)$ . The phase difference between two points $x_{1} = \frac{π}{3 k} a n d x_{2} = \frac{3 π}{2 k}$ is $ϕ_{1}$ for the standing wave and $ϕ_{2}$ for the travelling wave. If the ratio $\frac{ϕ_{1}}{ϕ_{2}} = \frac{3 a}{7 b}$ then $\frac{a}{b} =$

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Detailed Solution

For the stationary wave, $y_{1} = a \sin k x \cos ω t$

$\begin{aligned} x_{1} = \frac{π}{3 k} = \frac{λ}{6} < \frac{λ}{2}, and \\ x_{2} = \frac{3 π}{2 k} = \frac{3 λ}{4} > \frac{λ}{2} \end{aligned}$

$ϕ_{1} = π$

For the travelling wave,

$ϕ_{2} = k \times Δ x = \frac{7 π}{6}$

$\Rightarrow \frac{ϕ_{1}}{ϕ_{2}} = \frac{6}{7}$

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