The equations of two simple harmonic waves ar | vedclass

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

Question

(D) The standard equation for a wave is $Y = A \sin 2 \pi \left(\frac{t}{T} - \frac{x}{\lambda}\right)$.For the first wave: $Y_1 = 2 \sin 2 \pi \left(

Vedclass · Accepted Answer

same velocity

Vedclass · Answer

(D) The standard equation for a wave is $Y = A \sin 2 \pi \left(\frac{t}{T} - \frac{x}{\lambda}ight)$.For the first wave: $Y_1 = 2 \sin 2 \pi \left(\frac{4t}{0.2} - \frac{4x}{2}ight) = 2 \sin 2 \pi \left(\frac{t}{0.05} - \frac{x}{0.5}ight)$.Here,$T_1 = 0.05 	ext{ s}$ and $\lambda_1 = 0.5 	ext{ m}$.Velocity $v_1 = \frac{\lambda_1}{T_1} = \frac{0.5}{0.05} = 10 	ext{ m/s}$.For the second wave: $Y_2 = 4 \sin 2 \pi \left(\frac{4t}{0.16} - \frac{4x}{1.6}ight) = 4 \sin 2 \pi \left(\frac{t}{0.04} - \frac{x}{0.4}ight)$.Here,$T_2 = 0.04 	ext{ s}$ and $\lambda_2 = 0.4 	ext{ m}$.Velocity $v_2 = \frac{\lambda_2}{T_2} = \frac{0.4}{0.04} = 10 	ext{ m/s}$.Since $v_1 = v_2 = 10 	ext{ m/s}$,both waves have the same velocity.

The equations of two simple harmonic waves are given by $Y_1 = 2 \sin 8 \pi \left(\frac{t}{0.2} - \frac{x}{2}\right) \text{ m}$ and $Y_2 = 4 \sin 8 \pi \left(\frac{t}{0.16} - \frac{x}{1.6}\right) \text{ m}$. Then both waves have:

Similar Questions

$A$ travelling wave in a stretched string is described by the equation $y = A\sin (kx - \omega t)$. The maximum particle velocity is

The equation of a wave is $Y = 6 \sin(12 \pi t - 0.02 \pi x + \frac{\pi}{3})$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is: (in $m/s$)

$Assertion :$ Speed of wave $= \frac{\text{wavelength}}{\text{time period}}$
$Reason :$ Wavelength is the distance between two nearest particles in phase.

$A$ transverse wave in a medium is described by the equation $y = A \sin^2 (\omega t - kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to that of the wave velocity,if the value of $A$ is ($\lambda$ = wavelength of wave).

$A$ travelling acoustic wave of frequency $500 Hz$ is moving along the positive $x$-direction with a velocity of $300 ms^{-1}$. The phase difference between two points $x_{1}$ and $x_{2}$ is $60^{\circ}$. The minimum separation between the two points is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module