A longitudinal wave is represented by x = 10 | vedclass

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

Question

(B) The wave equation is given by $y = A \sin 2 \pi (nt - \frac{x}{\lambda})$.Here,the amplitude $A = 10 \, cm$.The maximum particle velocity is given

Vedclass · Accepted Answer

$5 \pi$

Vedclass · Answer

(B) The wave equation is given by $y = A \sin 2 \pi (nt - \frac{x}{\lambda})$.Here,the amplitude $A = 10 \, cm$.The maximum particle velocity is given by $V_{p, 	ext{max}} = \omega A = (2 \pi n) A$.The wave velocity is given by $V_{	ext{wave}} = n \lambda = \frac{\omega}{k} = \frac{2 \pi n}{2 \pi / \lambda} = n \lambda$.According to the problem,$V_{p, 	ext{max}} = 4 V_{	ext{wave}}$.Substituting the expressions: $(2 \pi n) A = 4 (n \lambda)$.Simplifying,we get $2 \pi A = 4 \lambda$.Therefore,$\lambda = \frac{2 \pi A}{4}$.Substituting $A = 10 \, cm$: $\lambda = \frac{2 \pi (10)}{4} = \frac{20 \pi}{4} = 5 \pi \, cm$.

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

Similar Questions

The phase difference between two points separated by $1 \ m$ in a wave of frequency $120 \ Hz$ is $90^o$. The wave velocity is .... $m/s$.

The relation between phase difference $(\Delta \phi)$ and path difference $(\Delta x)$ is:

The equation of a sound wave is $y = 0.0015 \sin (62.4x + 316t)$. The wavelength of this wave is ..... $unit$.

$A$ triangular pulse moving at $2 \ cm/s$ on a rope approaches an end at which it is free to slide on a vertical pole. What is the particle speed at the free end at $\frac{3}{4} \ s$ from the instant shown? (in $cm/s$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module