Question

progressive wave is represented by equation y=5 sin(80πt—0.5πx) where x,y are in meter and t in s. fine amplitude,wavelength,wave frequency and wave velo city

Answer 1

Answer: amplitude=5m

Wavelength=4m

Wave frequency=0.025 sec

Explanation: amplitude=5m will get easily from the standard equation i.e,y=Asin(wt-kx)

To find Wavelength,

K=0.5π(from standard equation)

K=0.5π

2π/∆=0.5π. (∆=lembda)

∆=2/0.5

∆=44m

Answer 2

Given that,

The progressive wave is represented by equation,

$y=5\sin (80\pi t-0.5\pi x)$ ......(1)

Where x,y are in meters

Solution,

The general equation of the progressive wave is given by :

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

A is amplitude of wave

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

Amplitude of wave is 5 meters

Angular frequency,

$\omega=80\pi\\\\2\pi f=80\pi\\\\f=40\ Hz$

Propagation constant,

$k=0.5\pi\\\\\dfrac{2\pi}{\lambda}=0.5\pi\\\\\lambda=4\ m$

Wave velocity,

$v=f\lambda\\\\v=40\times 4\\\\v=160\ m/s$

Hence, this is the required solution.

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Progressive wave

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