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Vika [28.1K]
4 years ago
8

A wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2

s. What is the wave equation (in base SI units) that correctly describes this wave
Physics
1 answer:
vladimir2022 [97]4 years ago
4 0

Explanation:

It is given that,

Wavelength of a wave, \lambda=35\ cm=0.35\ m

Amplitude, A=8.4\ cm

Period of the wavelength, t = 1.2 s

The wave is traveling in a string in the positive x direction. We need to write the wave equation for this conditions.

The general equation of the wave when it is traveling in +x direction is given by :

y=A\sin(kx-\omega t)

A is amplitude

k is propagation constant

k=\dfrac{2\pi}{\lambda}\\\\k=\dfrac{2\pi}{0.35}\\\\k=17.95\ m^{-1}\approx 18\ m^{-1}

\omega is angular frequency

\omega=\dfrac{2\pi}{T}\\\\\omega=\dfrac{2\pi}{1.2}\\\\\omega=5.23\ s^{-1}

So, the wave equation is given by :

y(x,t)=(0.084) \sin (18 x - 5.2 t)

Hence, this is the required solution.

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