A simple harmonic wave is expressed by equation: y=7 10^ -6 (800 … - Vidyadip

Question

A simple harmonic wave is expressed by equation:
$\text{y}=7\times10^{-6}\sin\Big(800\pi\text{t}-\frac{\pi}{42.5}\text{x}\Big)$
where y and x are in cm. and t in seconds. Calculate the following:

Amplitude.
Frequency.
Wavelength.
Wave velocity.
Phase difference between two particles separated by 17.0cm.

✓

Answer

Comparing the given equation with
$\text{Y}=\text{A}\sin(\omega\text{t}-\text{kx}),$ we get

Amplitude $=\text{A}=7\times10^{-6}\text{cm}$
Frequency $=\text{v}=\frac{\omega}{2\pi}=\frac{800\pi}{2\pi}=400\text{Hz}$
Wavelength $=\lambda=\frac{2\pi}{\text{k}}=\frac{2\pi}{\Big(\frac{\pi}{42.5}\Big)}=85\text{cm}$
Wave velocity $=\nu=\frac{\omega}{\text{k}}=\frac{800\pi}{\Big(\frac{\pi}{42.5}\Big)}$

$=3400\text{cm s}^{-1}$

$=340\text{ms}^{-1}$

Using $=\frac{\phi}{2\pi}=\frac{\text{x}}{\lambda},$ we get

Phase difference $=\phi=\frac{2\pi}{85}\times17$

$=\frac{2\pi}{5}\text{radian}$

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