Question

The equation of a progressive wave for n wire is:
$Y=4sin\left[\frac{\pi }{2}(8t-\frac{X}{8})\right]$ if X and Y are measured in cm then velocity of wave is then

• A. $64cm/salong-Xdirection$
• B. $32cm/salong-Xdirection$
• C. $32cm/salong+Xdirection$
• D. $64cm/salong+Xdirection$

Answer 1

The correct option is A $64cm/salong-Xdirection$

Given that.

$y=4\sin \left[\frac{\pi }{2}(8t-\frac{x}{8})\right]$

Now, on comparing from general equation

$y=a\sin [kx-\omega t+\varphi ]$

Now, the frequency is

$f=\frac{\omega }{2\pi }$

$f=\frac{4\pi }{2\pi }$

$f=2$

Now, the wave length is

$\lambda =\frac{2\pi }{k}$

$\lambda =\frac{2\times 16\pi }{\pi }$

$\lambda =32m$

Now, the velocity is

$v=f\lambda$

$v=2\times 32$

$v=64cm/s$

Hence, the velocity of wave is $64cm/s$ in- x direction