(A) The general equation of a wave is $y = A \sin(kx + \omega t + \phi)$.Comparing this with the given equation $y = \sin(20 \pi x + 10 \pi t)$,we get

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

(A) The general equation of a wave is $y = A \sin(kx + \omega t + \phi)$.Comparing this with the given equation $y = \sin(20 \pi x + 10 \pi t)$,we get the wave number $k = 20 \pi \ rad/m$.The wavelength $\lambda$ is given by $\lambda = \frac{2 \pi}{k} = \frac{2 \pi}{20 \pi} = 0.1 \ m = 10 \ cm$.Points having the same oscillating speed in a wave are separated by a distance of $\frac{\lambda}{2}$ (or multiples thereof).Therefore,the minimum distance is $\frac{\lambda}{2} = \frac{10 \ cm}{2} = 5 \ cm$.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

Medium

The equation of a wave travelling on a string is $y = \sin(20 \pi x + 10 \pi t)$,where $x$ and $t$ are distance and time in $SI$ units. The minimum distance between two points having the same oscillating speed is (in $cm$)

JEE MAIN 2025 All JEE MAIN

A
$5.0$
B
$20$
C
$10$
D
$2.5$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Waves and Sound

Subtopic

Wave Equation and Characteristics of Waves

Previous Year

JEE MAIN 2025 Paper All JEE MAIN years →

$A$ transverse wave is represented by $y = 2 \sin(\omega t - kx) \ cm$. The value of wavelength (in $cm$) for which the wave velocity becomes equal to the maximum particle velocity is:

MediumJEE MAIN 2022

View Solution

When a sound wave of wavelength $\lambda$ is propagating in a medium,the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

DifficultTS EAMCET 2008

View Solution

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)

MediumKCET 2008

View Solution

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

Medium

View Solution

$A$ particle on the trough of a wave at any instant will come to the mean position after a time ($T =$ time period).

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The equation of a wave travelling on a string is $y = \sin(20 \pi x + 10 \pi t)$,where $x$ and $t$ are distance and time in $SI$ units. The minimum distance between two points having the same oscillating speed is (in $cm$)

Similar Questions

$A$ transverse wave is represented by $y = 2 \sin(\omega t - kx) \ cm$. The value of wavelength (in $cm$) for which the wave velocity becomes equal to the maximum particle velocity is:

When a sound wave of wavelength $\lambda$ is propagating in a medium,the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

The equation of a simple harmonic wave is given by $y = 6 \sin 2 \pi (2t - 0.1x)$,where $y$ and $x$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 \ mm$ apart at any instant is (in $^{\circ}$)

$A$ transverse wave is described by the equation $y = A \sin [2\pi (f t - x/\lambda ) ]$. The maximum particle velocity is equal to four times the wave velocity if:

$A$ particle on the trough of a wave at any instant will come to the mean position after a time ($T =$ time period).

Vedclass Test Series

Exam Paper Generator

Online Exam Module