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

Question

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 (A) 3 cm (B) 6 cm (C) 8 cm (D) 5 cm

Tardigrade Admin · Accepted Answer

The equation of stationary wave is y=2 a cos (2 π x/λ) sin (2 π t/T) Given, a=8 cm, n=30 Hz, v =180 cm / s T =(1/n)=(1/30) s, ∴ λ =v T=180 × (1/30) =6 cm

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

3 cm

6 cm

8 cm

5 cm

The equation of stationary wave is
$y = 2 a cos \frac{2 π x}{λ} sin \frac{2 π t}{T}$
Given, $a = 8 c m, n = 30 Hz$ ,
$v = 180 c m / s$
$T = \frac{1}{n} = \frac{1}{30} s,$
$∴ λ = v T = 180 \times \frac{1}{30}$
$= 6 c m$

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