Progressive Wave Equation

The equation of a wave is $y = 0.07\sin(12\pi x - 3000\pi t)$ where $x$ is in metre and $t$ is in second then $1$ m m

The equation of a plane progressive wave is $Y = 0.025\sin(100t + 0.25x)$. The frequency of this wave would be

The equation of wave motion is $Y = 6\sin\left(12\pi t - 0.02\pi x + \frac{\pi}{3}\right)$ where x is in metre and time in second. The velocity of the wave is

A traveling wave is described by the equation $y(x, t) = [0.05\sin(8x - 4t)]$ m

The velocity of the wave is [All the quantities are in SI unit]

The equation of a progressive wave is $Y = 3\sin\left[\pi\left(\frac{t}{3} - \frac{x}{5}\right) + \frac{\pi}{4}\right]$ where X and Y are in metre and time in second. Which of the following is correct?

The equation of a plane progressive wave is given by $y = 5\cos\pi\left(200t - \frac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ________ m/s.

A transverse wave on a string is described by $y = 3\sin(36t + 0.018x + \pi/4)$, where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ______ cm. (Nearest integer)

$(\pi = 3.14)$

A wave travelling in the positive $x$-direction having displacement along $y$-direction as $1$ m, wavelength $2\pi$ m and frequency Hz is represented by

$\frac{1}{\pi}$

The equation of a progressive wave is given by $y = 6\cos(100t - 4x)$ where $y$ is in $\mu$m, $x$ in metre and $t$ in second. The ratio of the maximum particle velocity to the velocity of wave is

In a sine wave, minimum distance between $2$ particles always having same speed is

Two points separated by $6$ cm on a string has phase difference of $60^\circ$. If frequency of oscillation is $500$ Hz, the velocity of the wave in $\frac{m}{s}$ is

The path difference between two waves $Y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$ and $Y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \Phi\right)$ is

Two points on a travelling wave having frequency $500$ Hz and velocity $300$ m/s are $60^\circ$ out of phase, then the minimum distance between the two points is

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

Two simple harmonic progressive waves have displacements $y_1 = 5\sin\left(\frac{2\pi x}{\lambda} - \omega t\right)$ and $y_2 = 5\cos\left(\frac{2\pi x}{\lambda} - \omega t + \frac{\pi}{6}\right)$. The phase difference between the two waves is

Two waves are represented as

and

The path difference between two waves is

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at given time interval of 0.01s is

A simple harmonic progressive wave is represented by $y = A\sin(120\pi t + 3x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3}$ radian is

Two waves are represented by the equations, $y_1 = a\sin(\omega t + kx + 0.57)$ m and $y_2 = a\cos(\omega t + kx)$ m, where $x$ is in metre and $t$ is in second. What is the phase difference between them? ($\pi = 3.14$)

The distance between two consecutive points with phase difference of $60^\circ$ in a wave of frequency $n$ is $x$ meter. The velocity with which wave is traveling is

For a travelling harmonic wave

$y(x, t) = 2.0\cos 2\pi(10t - 0.0080x + 0.35)$, where $x$ and $y$ are in cm and $t$ in $\text{s}$. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is:

A simple harmonic progressive wave is given by the equation $y = a\sin 2\pi\left(nt - \frac{x}{\lambda}\right)$. If the wave velocity is equal to $\frac{1}{6} \times$ (maximum particle velocity), then the wavelength $\lambda$ is $\{a =$ amplitude, $n =$ frequency, $t =$ time, $y =$ displacement, $x =$ distance$\}$

A transverse wave is propagating on the string. The linear density of vibrating string is $10^{-3}$ kg/m. The equation of the wave is $Y = 0.05\sin(x + 15t)$ where $x$ and $Y$ are in metre and time in second. The tension in the string is

The equation of a wave on a string of linear mass density $0.02$ kg m$^{-1}$ is

$Y = 0.01\sin\left[2\pi\left(\frac{t}{0.02} - \frac{x}{0.50}\right)\right]$ m. The tension in the string is

The equation of a progressive wave is $Y = 3\sin\left[\pi\left(\frac{t}{3} - \frac{x}{5}\right) + \frac{\pi}{4}\right]$ where x and y are in meter and time in second. Which of the following is correct?

Displacement of a wave is expressed as $x(t) = 5\cos\left(628t + \frac{\pi}{2}\right)\text{m}$. The wavelength of the wave when its velocity is $300\text{ m/s}$ is:

$(\pi = 3.14)$

The equation of a transverse wave travelling along a string is

$y(x, t) = 4.0\sin\left[20 \times 10^{-3}x + 600t\right]\text{mm}$, where $x$ is in mm and $t$ is in second. The velocity of the wave is:

A particle performs S.H.M. of amplitude 'A' and wavelength ' $\lambda$ ', Then the velocity of the wave (V) and the maximum particle velocity (v) are related as

The equation of wave is $y = 60\sin(1200t - 6x)$, where ' $y$ ' is in micron, ' $t$ ' is in second and ' $x$ ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is

The distance between two consecutive points with phase difference of $45^\circ$ in a wave of frequency 300 Hz is 4.0 m. The velocity of the travelling wave is (in $\text{km/s}$)

A progressive wave of frequency 400 Hz is travelling with velocity $336\text{ m/s}$. How far apart are the two points on a wave which are $60^\circ$ out of phase?

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is:

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

A transverse displacement of vibrating string is $y = 0.06\sin\left(\frac{2\pi}{3}x\right)\cos(120\pi t)$.

If the mass per unit length of a string is $4 \times 10^{-2}\text{ kg/m}$, then the tension in the string will be

A wave is given by $Y = 3\sin 2\pi\left(\frac{t}{0.04} - \frac{x}{0.01}\right)$ where Y is in cm. Frequency of the wave and maximum acceleration will be $(\pi^2 = 10)$

The displacement of a travelling wave $y = C\sin\frac{2\pi}{\lambda}(at - x)$ where $t$ is time, $x$ is distance and $\lambda$ is the wavelength, all in S.I. units. Then the frequency of the wave is

A plane progressive wave is given by $y = 2\cos 2\pi(330t - x)\text{m}$. The frequency of the wave is:

The displacement of a wave is given by $y = 0.002\sin(100t + x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in second. This represents a wave

Velocity of sound waves in air is $330\text{ m/s}$. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of $1.6\pi$. frequency of this wave is

The diagram shows the propagation of a progressive wave. A, B, C, D, E are five points on this wave

Which of the following points are in the same state of vibration?

A transverse wave travelling along a stretched string has a speed of $30\text{ m/s}$ and a frequency of 250 Hz. The phase difference between two points on the string 10 cm apart at the same instant is

The distance between two consecutive points with phase difference of $60^\circ$ in wave of frequency 500 Hz is 0.6 m. The velocity with which wave is travelling is

A progressive wave of frequency 400 Hz is travelling with a velocity $336\text{ m/s}$. How far apart are the two points which are $60^\circ$ out of phase?

The path difference between two waves $Y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$ and $Y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right)$ is

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 two waves?

Velocity of sound waves in air is $330\text{ m/s}$. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of $1.6\pi$. The frequency of this wave is

A string has mass per unit length of $10^{-6}\text{ kg/cm}$ The equation of simple harmonic wave produced in it is $Y = 0.2\sin(2x + 80t)\text{ m}$. The tension in the string is

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

The equation of wave is $Y = 6\sin\left(12\pi t - 0.02\pi x + \frac{\pi}{3}\right)$ where '$x$' is in $\text{m}$ and '$t$' in $\text{s}$. The velocity of the wave is

A travelling wave is described by the equation

$y(x, t) = [0.05\sin(8x - 4t)]$ m

The velocity of the wave is: [all the quantities are in SI unit]

The equation of wave is given by

$Y = 10^{-2}\sin 2\pi(160t - 0.5x + \pi/4)$

where $x$ and $Y$ are in $\text{m}$ and $t$ in $\text{s}$. The speed of the wave is ________ $\text{km h}^{-1}$.

A transverse harmonic wave on a string is given by

$y(x, t) = 5\sin(6t + 0.003x)$

where x and y are in cm and t in sec. The wave velocity is _______________ ms$-1$.

The equation of a progressive wave is $Y = a\sin 2\pi\left(nt - \frac{x}{5}\right)$. The ratio of maximum particle velocity to wave velocity is

A progressive wave is given by, $Y = 12\sin(5t - 4x)$. On this wave, how far away are the two points having a phase difference of $90^\circ$?

The displacement of two sinusoidal waves is given by the equation

$\begin{matrix} y_1 = 8\sin(20x - 30t) \\ y_2 = 8\sin(25x - 40t) \end{matrix}$

then the phase difference between the waves after time $t = 2\text{ s}$ and distance $x = 5\text{ cm}$ will be

The path difference between two waves, represented by $y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$ and $y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right)$ is

The distance between two consecutive points with phase difference of 60$^\circ$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s

A transverse wave $Y = 2\sin(0.01x + 30t)$ moves on a stretched string from one end to another end in 0.5 second. If $x$ and $y$ are in $\text{cm}$ and $t$ in second, then the length of the string is

A transverse wave in a medium is given by $y = A\sin 2(\omega t - kx)$. It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of $A$?

The equation of simple harmonic progressive wave is given by $y = a\sin 2\pi(bt - cx)$. The maximum particle velocity will be half the wave velocity, if $c =$

The equation of the wave is $Y = 10\sin\left(\frac{2\pi t}{30} + \alpha\right)$ If the displacement is $5\text{ cm}$ at $t = 0$ then the total phase at $t = 7.5\text{ s}$ will be $(\sin 30^\circ = 0.5)$

In the wave equation

$y = 0.5\sin\frac{2\pi}{\lambda}(400t - x)\text{ m}$

the velocity of the wave will be:

Which of the following equations correctly represents a travelling wave having wavelength $\lambda$ = 4.0 cm, frequency $\nu$ = 100 Hz and travelling in positive x-axis direction?

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

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

Equation 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

Which of the following equations represents a travelling wave?

Velocity of sound waves in air is '$V$' $\text{m/s}$. For a particular sound wave in air, path difference of 'x' $\text{cm}$ is equivalent to phase difference $n\pi$. The frequency of this wave is

Two waves are represented by the equation, $y_1 = A\sin(\omega t + kx + 0.57)\text{m}$ and $y_2 = A\cos(\omega t + kx)\text{m}$, where $x$ is in metre and $t$ is in second. What is the phase difference between them?

A sound wave of frequency $160\text{ Hz}$ has a velocity of $320\text{ m/s}$. When it travels through air, the particles having a phase difference of $90^\circ$, are separated by a distance of

A sound wave is travelling with a frequency of $50\text{ Hz}$. The phase difference between the two points in the path of a wave is $\frac{\pi}{3}$. The distance between those two points is (Velocity of sound in air $= 330\text{ m/s}$)

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is

A transverse wave given by $y = 2\sin(0.01x + 30t)$ moves on a stretched string from one end to another end in 0.5 second. If '$x$' and '$y$' are in $\text{cm}$ and '$t$' is in second, then the length of the string is

A sound wave of frequency 245 Hz travels with the speed of 300 ms${}^{-1}$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

A simple harmonic progressive wave is given by $Y = Y_0\sin 2\pi\left(nt - \frac{x}{\lambda}\right)$. If the wave velocity is $\left(\frac{1}{8}\right)$th the maximum particle velocity then the wavelength is

The equation of wave is given by $y = 10\sin\left(\frac{2\pi t}{30} + \alpha\right)$. If the displacement is $5\text{ cm}$ at $t = 0$, then the total phase at $t = 7.5\text{ s}$ will be

$\left[\sin 30^\circ = \cos 60^\circ = \frac{1}{2}, \cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3}}{2}\right]$

The equation of simple harmonic wave produced in the string under tension $0.4\text{ N}$ is given by $y = 4\sin(3x + 60t)\text{ m}$. The mass per unit length of the string is

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $-$ 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x $\times$ 10$-$2 N. Value of x is _________. (Round off to the nearest integer)

The amplitude of wave disturbance propagating in the positive x-direction is given by $y = \frac{1}{1 + x^2}$ at time t = 0 and $y = \frac{1}{1 + (x - 2)^2}$ at t = 1 s, where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ___________ m/s.

A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in metre and t is in seconds. Which of the following is a correct statement about the wave?

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