Question

Two points on string are being observed as a travelling wave passes them. Then point are at $x_1=0$ a $x_2=1m$, the transverse motions of two points are found to be as follows.

$y_1=A\sin \left(3\pi t\right)$ and $y_2=A\sin \left(3\pi t+\frac{\pi }{8}\right)$t is in seconds and y in metre. Mark correct options.

• A. Frequency of wave is $3Hz$
• B. Frequency of wave is $1.5Hz$
• C. Wavelength may be $16m$
• D. Wavelength may be $\frac{16}{17}m$

Answer 1

The correct option is B Frequency of wave is $1.5Hz$

$y_1=A\sin \left(3\pi t\right)$

$y_2=A\sin (3\pi t+\frac{\pi }{8})$

Frequency of the wave will always remain constant wherever it is in the x direction. Since general equation is

$y=A\sin \left(\omega t\right)$

On comparing,

$\omega =3\pi$

$2\pi f=3\pi$

$f=\frac{3\pi }{2\pi }=1.5Hz$