Waves Ques 36
36. A transverse wave is represented by $y=A \sin$ $(\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?
[2010]
(a) $\frac{\pi A}{2}$
(b) $\pi A$
(c) $2 \pi A$
(d) $A$
Show Answer
Answer:
Correct Answer: 36.(c)
Solution:
- (c) $y=A \sin (\omega t-k x)$
Particle velocity,
$v_p=\frac{d y}{d t}=A \omega \cos (\omega t-k x)$
$\therefore \quad v _{p \max }=A \omega$
wave velocity $=\frac{\omega}{k}$
$\therefore A \omega=\frac{\omega}{k}$
i.e., $A=\frac{1}{k}$ But $k=\frac{2 \pi}{\lambda}$
$\therefore \quad \lambda=2 \pi A$
BETA
