A transverse wave given by $\mathrm{y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$ moves on a stretched string…
A transverse wave given by $\mathrm{y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$ moves on a stretched string from one end to another end in 0.5 second. If ' $x$ ' and ' $y$ ' are in $\mathrm{cm}$ and ' $\mathrm{t}$ ' is in second, then the length of the string is
6m
9m
12m
15m
Solution
Comparing with the standard equation
$\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t})$
we get $\mathrm{k}=0.01 \mathrm{rad} / \mathrm{cm}$ and $\omega=30 \mathrm{rad} / \mathrm{s}$
speed of the wave, $v=\frac{\omega}{\mathrm{k}}=\frac{30}{0.01}=300 \mathrm{~cm} / \mathrm{s}=30 \mathrm{~m} / \mathrm{s}$
$\therefore$ Distance $=\mathrm{vt}=30 \times 0.5=15 \mathrm{~m}$