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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Similar Questions

The distance between two consecutive points with a phase difference of $60^{\circ}$ in a wave of frequency $n$ is $x$ meters. The velocity with which the wave is traveling is:

For a wave equation given by $y = 2 \sin \pi (0.5x - 200t) \, cm$,what is the wave velocity in $cm/sec$?

The figure shows the wave $y = A \sin(\omega t - kx)$. What is the magnitude of the slope of the curve at $B$?

The equation of a transverse wave is given by $y = 100 \sin \pi (0.04z - 2t)$,where $y$ and $z$ are in $cm$ and $t$ is in seconds. The frequency of the wave in $Hz$ is

The two waves represented by $y_1 = a \sin(\omega t)$ and $y_2 = b \cos(\omega t)$ have a phase difference of

Vedclass Test Series

Exam Paper Generator

Online Exam Module