Question

Transverse waves of amplitude $0.05m$ are generated at one end of a long string $(x=0)$. At a certain instant of time the displacement of particle $A$ at $x=1m$ is $-5cm$ and of particle $B$ at $x=2m$ is $+5cm$. What is the wavelength of waves?

Answer 1

Amplitude $=0.05$m$=5$m

Points A & B can be

Point A is a trough & Point B is a rest, as shown in figure

As, it isn't given whether A & B are consecutive rests and troughs

$d(A.B)=(n+\frac{1}{2})\cdot \lambda$ ........(i)

Distance between a crest & a trough

where $n=0,1,2,.....$

Given distance between A & B$=1$m

From (i)

$(n+\frac{1}{2})\lambda =1$

$\Rightarrow \lambda =\frac{1}{(n+\frac{1}{2})}m$

$n=0,1,2,....$

For the simplest case: $n=0$ adjacent rest & trough.

$\lambda =2m$.