A wave is represented by the equation y = 10 | vedclass

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

Question

(B) The given equation is $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$.Using the trigonometric identity $\sin C + \sin D = 2 \sin(\fr

Vedclass · Accepted Answer

$20$ units and $25$ units

Vedclass · Answer

(B) The given equation is $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$.Using the trigonometric identity $\sin C + \sin D = 2 \sin(\frac{C+D}{2}) \cos(\frac{C-D}{2})$,we get:$y = 10 [2 \sin(2\pi \cdot 100t) \cos(2\pi \cdot 0.02x)]$.$y = 20 \sin(200\pi t) \cos(0.04\pi x)$.Comparing this with the standard standing wave equation $y = A_{max} \sin(\omega t) \cos(kx)$,the maximum amplitude $A_{max} = 20$ units.The wave number $k = 0.04\pi$. Since $k = \frac{2\pi}{\lambda}$,we have $\frac{2\pi}{\lambda} = 0.04\pi$.$\lambda = \frac{2}{0.04} = 50$ units.The loop length is defined as $\frac{\lambda}{2} = \frac{50}{2} = 25$ units.Thus,the maximum amplitude is $20$ units and the loop length is $25$ units.

$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

Similar Questions

The following equations represent progressive transverse waves:
$Z_1 = A \cos(\omega t - kx)$,
$Z_2 = A \cos(\omega t + kx)$,
$Z_3 = A \cos(\omega t + ky)$,
$Z_4 = A \cos(2\omega t - 2ky)$.
$A$ stationary wave will be formed by superposing:

$A$ stationary wave is represented by $y = A \sin(100t) \cos(0.01x)$,where $y$ and $A$ are in millimetres,$t$ is in seconds,and $x$ is in metres. The velocity of the constituent wave is ........... $m/s$.

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40\pi t$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is..... $cm$.

Spacing between two successive nodes in a standing wave on a string is $x$. If the frequency of the standing wave is kept unchanged but the tension in the string is doubled,then the new spacing between successive nodes will become

For the stationary wave $y = 4 \sin \left(\frac{\pi x}{15}\right) \cos (96 \pi t)$,the distance between a node and the next antinode is

Vedclass Test Series

Exam Paper Generator

Online Exam Module