Waves

Step: Find the wavelength of the transmitted wave.
The frequency of the wave pulse remains unchanged since it depends only on the source. The wavelength of the transmitted wave is given by;
\(\frac{\lambda_1}{\lambda_2}=\frac{v_2}{v_1}\)
\(\Rightarrow \frac{\lambda_1}{\lambda_2}= \sqrt{\frac{\mu_2}{\mu_1}}~~~~~~~~~~~~\left[v=\sqrt{\frac{T}{\mu}}\right]\)
\(\Rightarrow \frac{\lambda_1}{\lambda_2}=\frac{1}{2}\)
\(\Rightarrow \lambda_2=2\lambda _1=80~\text{cm}\)
Hence, option (2) is the correct answer.
 

Step: Identify the equations of given waves.
\(Y_{A}=A\sin\omega t \\ Y_{B}=A\sin\left ( \omega t+\pi /2 \right ) \\ Y_{C}=A\sin\left ( \omega t-\pi /2 \right )\)
So, from above, it is clear that the wave \(C\) lags behind in phase by \(\pi/2\) and \(B\) leads by \(\pi/2\).
Hence, option (1) is the correct answer.