A simple harmonic progressive wave is represe | vedclass

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

Question

(B) The given equation of the $SHM$ wave is $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. Expanding this,we get $y = 0.03 \sin (2 \pi t - 0.01 \pi x) \ m$.

Vedclass · Accepted Answer

$\frac{\pi}{4} \ rad$

Vedclass · Answer

(B) The given equation of the $SHM$ wave is $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. Expanding this,we get $y = 0.03 \sin (2 \pi t - 0.01 \pi x) \ m$. Comparing this with the general wave equation $y = a \sin (\omega t - k x)$,we identify the wave number $k$ as $k = 0.01 \pi \ rad/m$. The phase difference $\Delta \phi$ between two particles separated by a distance $\Delta x$ is given by the formula $\Delta \phi = k \Delta x$. Given $\Delta x = 25 \ m$ and $k = 0.01 \pi \ rad/m$,we substitute these values into the formula: $\Delta \phi = (0.01 \pi) 	imes 25 = 0.25 \pi = \frac{\pi}{4} \ rad$. Thus,the phase difference is $\frac{\pi}{4} \ rad$.

$A$ simple harmonic progressive wave is represented as $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. At a given instant of time,the phase difference between two particles $25 \ m$ apart is

Similar Questions

Two simple harmonic progressive waves have displacements $y_1 = a_1 \sin \left(\frac{2 \pi x}{\lambda} - \omega t\right)$ and $y_2 = a_2 \cos \left(\frac{2 \pi x}{\lambda} - \omega t + \phi\right)$. What is the phase difference between the two waves?

When a wave travels in a medium,the particle displacement is given by $y(x, t) = 0.03 \sin \pi (2t - 0.01x)$,where $y$ and $x$ are in meters and $t$ is in seconds. The phase difference,at a given instant of time,between two particles $25 \ m$ apart in the medium is:

$A$ sinusoidal wave of wavelength $7.5 \ cm$ travels a distance of $1.2 \ cm$ along the $x$-direction in $0.3 \ s$. The crest $P$ is at $x = 0$ at $t = 0 \ s$ and the maximum displacement of the wave is $2 \ cm$. Which equation correctly represents this wave?

The phase difference between two points separated by $0.8 \ m$ in a wave of frequency $120 \ Hz$ is $\frac{\pi}{2}$. The velocity of the wave is ..... $m/s$.

The equation of wave motion is $Y = 5 \sin (10 \pi t - 0.02 \pi x + \pi / 3)$ where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is (in $m/s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module