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Q.
Two mechanical waves $y_{1}=2 \sin 2 \pi(50 t-2 x) \& y_{2}=$ $4 \sin 2 \pi(a x+100 t)$ propagate in a medium with same speed. Choose the correct statement.
Waves
Solution:
$V _{1}= V _{2}$
$\frac{2 \pi \times 50}{2 \pi \times 2}=\frac{2 \pi \times 100}{2 \pi a }$
$\Rightarrow \frac{ I _{1}}{ I _{2}}=\frac{ a _{1}^{2} n _{1}^{2}}{ a _{2}^{2} n _{2}^{2}}$
$\frac{50}{2}=\frac{100}{ a }$
$=\frac{2^{2}}{4^{2}} \times \frac{(2 \pi \times 50)}{(2 \pi \times 100)^{2}}$
$\therefore a =4 =\frac{1}{4} \times \frac{1}{4}$
$\Rightarrow \left\{\frac{I_{1}}{I_{2}}=\frac{1}{16}\right\}$