A sound wave of frequency 210 text{ Hz} trave | vedclass

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(B) The general equation of a progressive wave is $s(x, t) = A \sin(kx - \omega t)$.$1$. Amplitude $(A)$: The particle moves $10 	ext{ cm}$ between t

Vedclass · Accepted Answer

$s(x, t)=0.05 \sin [4 x-1320 t] 	ext{ m}$

Vedclass · Answer

(B) The general equation of a progressive wave is $s(x, t) = A \sin(kx - \omega t)$.$1$. Amplitude $(A)$: The particle moves $10 	ext{ cm}$ between two extreme points, which is the total path length $(2A)$. Thus, $2A = 10 	ext{ cm} = 0.10 	ext{ m}$, so $A = 0.05 	ext{ m}$.$2$. Angular frequency $(\omega)$: $\omega = 2\pi f = 2 	imes \pi 	imes 210 = 420\pi \approx 1319.47 \approx 1320 	ext{ rad/s}$.$3$. Wave number $(k)$: $v = \frac{\omega}{k} \implies k = \frac{\omega}{v} = \frac{420\pi}{330} = \frac{42\pi}{33} = \frac{14\pi}{11} \approx 4 	ext{ rad/m}$.$4$. Substituting these values into the wave equation: $s(x, t) = 0.05 \sin(4x - 1320t) 	ext{ m}$.

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