Question

the equation for the wave travelling along the +x axis with velocity 350 $m{s}^{-1}$ when its position at t=0 is as shown

• A. $0.05\sin (\frac{314}{4}x-27475t)$
• B. $0.05\sin (\frac{379}{5}x-27475t)$
• C. $1\sin (\frac{314}{4}x-27475t)$
• D. $0.05\sin (\frac{289}{5}x+27475t)$

Answer 1

The correct option is A $0.05\sin (\frac{314}{4}x-27475t)$

From the given wave diagram,

A=$0.05m$

& $2\lambda +\frac{\lambda }{2}=0.2\Rightarrow \frac{5\lambda }{2}=0.2\lambda =\frac{0.4}{5}=0.08m$

Now, wave velocity=$350m/s$ (given)

$V_w=\frac{w}{k}350=\frac{w}{2\pi /\lambda }\Rightarrow w=\frac{2\pi }{\lambda }\times 350w=\frac{2\pi \times 350}{0.08}=27488.93\approx 27475$

Let the equation for this wave be

$y=A\sin (kx-wt)y=0.05\sin (\frac{2\pi }{\lambda }-27475t)y=0.05\sin (\frac{100\times 3.14}{4}x-27475t)[y=0.05\sin (\frac{314}{4}x-27475t)]$

Hence option (A) is correct