Question

A wave travelling along a string is described by the equation y(x,t)=0.05sin(40x-5t) in which numerical constants are SI units(0.05m, 40 rad/m and 5rad/s). What is the wavelength?

Answer 1

$2\pi \div \gamma = 40$

$\gamma = \pi \div 20$

Answer 2

Given that,

A wave travelling along a string is described by the equation :

$y(x,y)=0.05\sin (40x-5t)$ ......(1)

To find,

Wavelength of wave.

Solution,

The general equation of wave travelling along a string is given by :

$y=A\sin (kx-\omega t)$ .....(2)

On comparing equation (1) and (2) we get :

k = 40 rad/m

Since,

$k=\dfrac{2\pi}{\lambda}\\\\\lambda=\dfrac{2\pi}{k}\\\\\lambda=\dfrac{2\pi}{40}\\\\\lambda=0.157\ m$

So, the wavelength of a wave is 0.157 meters.

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