KEAM 2018

A wave pulse in a string is described by the equation $y_1=\frac{5}{{\left(3x-4t\right)}^2+2}$ and another wave pulse in the same string is described by $y_2=\frac{-5}{{\left(3x+4t-6\right)}^2+2}$ . The values of $y_1,y_2$ and $x$ are in metres and $t$ is in seconds. Which of the following statement is correct?

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a $\mathrm{o}\mathrm{n}\mathrm{e}-\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}$ string are $\mathrm{1 }m{s}^{-1}$ and $1 m{s}^{-2}$ respectively. The phase velocity of the wave is $\mathrm{1 }m{s}^{-1}$ . The waveform is

The displacement $y$ of a particle, if given by $y=4{\cos }^2\left(\frac{t}{2}\right)\sin \left(1000 t\right).$ This expression may be considered to be a result of the superposition of how many simple harmonic motions?

Two strings of the same material and same length are given equal tension. If they are vibrating with fundamental frequencies $1600\mathrm{Hz}$ and $900\mathrm{Hz},$ then the ratio of their respective diameters is

A travelling wave in a medium is given by the equation $\mathrm{y}=\mathrm{asin} (\mathrm{\omega t}-\mathrm{kx})$. The maximum acceleration of the particle in the medium is

Consider a wire with density $\left(d\right)$ and stress $\left(\sigma \right).$ For the same density, if the stress increases $2$ times, the speed of the transverse waves along the wire changes by

The displacement of a wave is represented by $y=0.6\times {10}^{-3}\sin \left(500t-0.05x\right),$ where all the quantities are in their proper units. The maximum particle velocity $\left(\mathrm{i}\mathrm{n}\mathrm{ }m{s}^{-1}\right)$ of the medium is