Question
Write the equation of a progressive wave propagating along the positive x -direction, whose amplitude is 5 cm , frequency 250 Hz and velocity $500 ms^{-1}$.
✓
Answer
Here $A =5 cm=0.05 m, v =250 Hz, \nu=500 ms^{-1}$
Wavelength, $\lambda=\frac{v}{\nu}=\frac{500}{250}=2 m$
Period, $T=\frac{1}{v}=\frac{1}{250} s$
The equation for the given wave can be written as $y =A \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right)=0.05 \sin 2 \pi\left(250 t-\frac{x}{2}\right)$
or $y=0.05 \sin \times(500 t-x)$ metre
Wavelength, $\lambda=\frac{v}{\nu}=\frac{500}{250}=2 m$
Period, $T=\frac{1}{v}=\frac{1}{250} s$
The equation for the given wave can be written as $y =A \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right)=0.05 \sin 2 \pi\left(250 t-\frac{x}{2}\right)$
or $y=0.05 \sin \times(500 t-x)$ metre
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