Terms in Wave Motion

Two plane-progressive waves in the same phase must have:

Light waves travel in the form of _____waves.

Progressive waves are waves originating from a source such that they never return to the source.

The equation of a progressive wave is $Y=a\sin (\omega t-kx)$, then the velocity of the wave is

The displacement $y$ of a wave travelling in the $x$-direction is given by $y={10}^{-4} \sin \left(600t-2x+\frac{\mathrm{\pi }}{3}\right) \mathrm{m}$, where $x\text{ and} t$ are in SI unit. What is the speed (In SI unit) of the wave?

A uniform solid cylinder can roll without sliding on a horizontal surface as shown in the figure. The mass of cylinder is $10 \mathrm{kg}$ and the spring constant for both the ideal springs is $300 \mathrm{N} {\mathrm{m}}^{-1}$. What is the angular frequency (in $\mathrm{rad} {\mathrm{s}}^{-1}$) of small oscillations of the centre of the cylinder?

On an average, a human heart is found to beat $72$ times a minute. Its frequency and period are

A point particle is acted upon by a restoring force $-k{x}^3.$ The time period of oscillation is $T$ when the amplitude is $A.$ The time period for an amplitude $2 A$ will be:

Monochromatic light of frequency $5\times {10}^{14} \mathrm{Hz}$ travelling in vacuum enters a medium of refractive index $1.5$. Its wavelength in the medium is

A point particle is acted upon by a restoring force $-k{x}^3.$ The time period of oscillation is $T$ when the amplitude is $A.$ The time period for an amplitude $2A$ will be:

Compare the velocities of the waveforms given below, and choose the correct option.

The diagram shows the propagation of a wave. Which points are in same phase?

The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency $n$.

Consider the following statements:

Two waves meet at a point. The waves have a path difference of $\frac{\lambda }{4}.$ The phase difference between the waves is

A particle of mass $\frac{2}{3} \mathrm{kg}$ with velocity $v=-15 \mathrm{m} {\mathrm{s}}^{-1}$ at $t=-2 \mathrm{s}$ is acted upon by a force $F=k-\beta t^2$. Here, $k=8 \mathrm{N}$ and $\beta =2 \mathrm{N} {\mathrm{s}}^{-2}$. The motion is one-dimensional. Then, the speed at which the particle acceleration is zero again, is

A ball is moving uniformly in a circular path of radius $1 \mathrm{m}$ with a time period of $1.5 \mathrm{s}$. If the ball is suddenly stopped at $t=8.3 \mathrm{s},$ the magnitude of the displacement of the ball with respect to its position at $t=0 \mathrm{s}$ is closest to:

The frequency of tuning fork is $500 \mathrm{Hz}$ and the velocity of sound in air is $300 \mathrm{m} {\mathrm{s}}^{-1}$. The distance travelled by sound while the fork executes $100$oscillations per second is ______.

A uniform string of length $L$ and mass $M$ hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance $x$ from the free end is

Two strings $P$ and $Q$ made of same material are stretched by same tension. The radius of string $P$ is half of the radius of $Q.$ A transverse wave travels on $P$ with speed $v_P$ and on $Q$ with speed $v_Q$. The ratio of $v_P$ and $v_Q$ is

Transverse waves are generated in two uniform wires $A$ and $B$ of the same material by attaching their free ends to a vibrating source of frequency $200 \mathrm{Hz}$. The cross-sectional area of $A$ is half that of $B$ while the tension on $A$ is twice that on $B$. The ratio of the wavelengths of the transverse waves in $A$ and $B$ is :