Question

A transverse sine wave of amplitude $10cm$ and wavelength $200cm$ travels from left to right along a long horizontal stretched string with a speed of $100cm/s$. Take the origin at left end of the string. At time $t=0$, the left end of the string is at the origin and is moving downward. Then the equation of the wave will be (in C.G.S. system)

• A. $10\sin (0.01\pi x-\pi t)$
• B. $10\sin (0.02\pi x-\pi t)$
• C. $10\sin (0.01x-\pi t)$
• D. $10\sin (0.02x-\pi t)$

Answer 1

The correct option is A $10\sin (0.01\pi x-\pi t)$

Amplitude $A=10cm$

angular wave number $k=2\pi /\lambda =2\pi /200cm=0.01\pi c{m}^{-1}$

velocity of wave $v=\lambda \times \nu =100\Rightarrow \nu =100/200=0.5Hz$

angular frequency $\omega =2\pi \nu =\pi Hz$

Now at $t=0$, the origin is at left end

i.e. at $x=0andt=0,y=0$ so initial phase angle $\varphi =0$

The left end is moving downwards as time increases, This means origin is moving to right side(+ve x-axis) as time increases, so wave is moving in positive x-direction.

So equation of wave is given as $y(x,t)=A\sin (kx-\omega t+\varphi )$

using values calculated above,

$y(x,t)=10\sin (0.01\pi x-\pi t)cm$ (in CGS system)