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  4. The component waves producing a stationary wave have amplitude, frequency and velocity are respectively 8 cm, 30 Hz and 180 cm/s. The wavelength of the wave is

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Q. The component waves producing a stationary wave have amplitude, frequency and velocity are respectively $8\, cm,\, 30\, Hz$ and $180\, cm/s$. The wavelength of the wave is

AMUAMU 2001

Solution:

The equation of stationary wave is
$y=2 a \cos \frac{2 \pi x}{\lambda} \sin \frac{2 \pi t}{T}$
Given, $a=8\, cm,\, n=30\, Hz$,
$v =180\, cm / s$
$T =\frac{1}{n}=\frac{1}{30} s,$
$\therefore \lambda =v T=180 \times \frac{1}{30}$
$=6\, cm$