Question

Two mechanical waves $y_1=2\sin 2\pi (50t-2x)\&y_2=$ $4\sin 2\pi (ax+100t)$ propagate in a medium with same speed. Choose the correct statement.

• A. The ratio of their intensities is 1 : 16
• B. The ratio of their intensities is 1 :4
• C. The value of ‘a’ is 3 units
• D. The value of ‘a’ is 2 units

Answer 1

Answer: (A)

$V_1=V_2$
$\frac{2\pi \times 50}{2\pi \times 2}=\frac{2\pi \times 100}{2\pi a}$
$\Rightarrow \frac{I_1}{I_2}=\frac{a_1^2{n}_1^2}{a_2^2{n}_2^2}$
$\frac{50}{2}=\frac{100}{a}$
$=\frac{2^2}{4^2}\times \frac{(2\pi \times 50)}{(2\pi \times 100{)}^2}$
$\therefore a=4=\frac{1}{4}\times \frac{1}{4}$
$\Rightarrow \left\{\frac{I_1}{I_2}=\frac{1}{16}\right\}$