A wave is represented by the equation -y=(0.001mm) [(50s^ -1 )t+(… - Vidyadip

MCQ

A wave is represented by the equation $-\text{y}=(0.001\text{mm})\sin\Big[(50\text{s}^{-1})\text{t}+(2.0\text{m}^{-1})\text{x}\Big]$

The wave velocity $= 100m/s.$
The wavelength $= 2.0m.$
The frequency $=\frac{25}{\pi}\text{Hz}$
The amplitude $= 0.001mm.$

A
$a$ and $ b$
B
$a$ and $c$
C
$c$ and $d$
D
$b$ and $d$

✓

Answer

$\text{y}=(0.001\text{mm})\sin\Big[(50\text{s}^{-1})\text{t}+(2.0\text{m}^{-1})\text{x}\Big]$

Equating the above equation with the general equation, we get:
$\text{y}=\text{A}\sin(\omega\text{t}-\text{kx})$
$\omega=\frac{2\pi}{\text{T}}=2\pi\nu$
$\text{k}=\frac{2\pi}{\lambda}$
Here. $A $ is the amplitude, $\omega$ is the angular frequency, $k$ is the wave number and $\lambda$ is the wavelength.
$\text{A}=0.001\text{mm}$
Now,
$50=2\pi\nu$
$\Rightarrow\nu=\frac{25}{\pi}\text{Hz}$

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