Question

Two points on string are being observed as a travelling wave passes from them. The points are at $x_1=0$ and $x_2=1\text{m}$, the transverse motions of two points are found to be as follows $y_1=\text{A sin}\left(3\pi t\right)$ and $y_2=\text{A sin}(3\pi t+\frac{\pi }{8})$; t is in seconds and y in metre. Mark the correct option(s)

• A. Frequency of wave is 3 Hz
• B. Frequency of wave is 1.5 Hz
• C. Wavelength may be 16 m
• D. Wavelength may be $\frac{16}{15}\text{m}$

Answer 1

Answer: (B), (C)

The correct options are
B

Frequency of wave is 1.5 Hz

C

Wavelength may be 16 m

$y_1=\text{A}\text{sin}3\pi \text{t}$

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

$\therefore \varphi =\frac{\pi }{8}$ and $2\pi v=3\pi$ $\therefore v=1.5$

As $\text{k}=\frac{\omega }{v}$ and $\varphi =\text{kx}$ $\therefore \frac{3\pi }{v}\times 1=\frac{\pi }{8}$

$\Rightarrow \text{v}=24m/s$ $\therefore \lambda =\frac{24\times 2}{3}=16\text{m}$