Question

A transverse wave of amplitude 0.5 m and wave length 1m and frequency 2 hertz is propagating in a string in the negative x direction.The expression of this wave is

Answer 1

Answer:

A transverse wave of amplitude 0.5 m and wavelength 1m and frequency 2 hertz is propagating in a string in the negative x-direction. The expression of this wave is $y=0.5 \sin (2 \pi x+4 \pi t)$

Explanation:

Equation of transverse wave propagating in the negative x-direction is given by,

$y=A \sin (k x+w t)$

Where,  

A - Amplitude of the wave

k - Wave vector ;    $\mathrm{k}=\frac{2 \pi}{\lambda}$

λ - Wavelength

x - Distance

W -  Angular frequency;    w = $2\pi f$

f  -  Frequancy

Given,

A = 0.5 m           λ = 1 m           f = 2 Hz

$\mathrm{k}=\frac{2 \pi}{\lambda}=\frac{2 \pi}{1}=2 \pi$

$\mathrm{w}=2 \pi \mathrm{v}=2 \pi \times 2=4 \pi$

Substituting the above values into the standard equation

The expression of the wave is,

$y=0.5 \sin (2 \pi x+4 \pi t)$