JEE Main - 12th January 2019 Shift 1

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

A wire of length $30 \mathrm{cm}$, stretched between rigid supports, has its $n^{\mathrm{th} }$ and ${\left(n+1\right)}^{\mathrm{th}}$ harmonics at $400 \mathrm{Hz}$ and $450 \mathrm{Hz}$, respectively. If tension in the string is $2700 \mathrm{N}$, its linear mass density is _____ $\mathrm{kg} {\mathrm{m}}^{-1}$.

In the wave equation $y=0.5\sin \frac{2\pi }{\lambda }\left(400t-x\right)m$ the velocity of the wave will be :

The distance between two consecutive points with phase difference of $60°$ in a wave of frequency $500 \mathrm{Hz}$ is $6.0 \mathrm{m}$. The velocity with which wave is travelling is ______ $\mathrm{km} {\mathrm{s}}^{-1}$.

Two simple harmonic waves having equal amplitudes of $8 \mathrm{cm}$ and equal frequency of $10 \mathrm{Hz}$ are moving along the same direction. The resultant amplitude is also $8 \mathrm{cm}$. The phase difference between the individual waves is _____ degree.

For a solid rod, the Young's modulus of elasticity is $3.2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$ and density is $8\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$. The velocity of longitudinal wave in the rod will be

A steel wire with mass per unit length $7.0 \times {10}^{–3} \mathrm{kg} {\mathrm{m}}^{–1}$ is under tension of $70 \mathrm{N}$. The speed of transverse waves in the wire will be:

A travelling wave is described by the equation $y\left(x,t\right)=\left[0.05\sin \left(8x-4t\right)\right] \mathrm{m}$. The velocity of the wave is:

[All the quantities are in SI unit]