G L Mittal and TARUN MITTAL Solutions for Chapter: Progressive Harmonic Waves, Exercise 2: NUMERICALS

The displacement equation of a transverse wave in a string is expressed as $y=1.5 \sin \mathrm{\pi } \left(6 t+0.002 x\right)$, where y and x are expressed in cm and t in second. Find the speed of the wave.

The displacement equation of a transverse wave in a string is expressed as $y=1.5 \sin \mathrm{\pi } \left(6 t+0.002 x\right)$, where $y$ and $x$ are expressed in $\mathrm{cm}$ and $t$ in second. Find the frequency of the wave.

A wave whose amplitude is $0.2 \mathrm{mm}$ and frequency is $500 {\mathrm{s}}^{-1}$ travels in air with a velocity of $350 \mathrm{m} {\mathrm{s}}^{-1}$. Determine the displacement of the particle situated at a distance of $3.5$ from the origin in the direction of the wave at the instant $t = 0.05 \mathrm{s}$.

A progressive wave in a string is expressed by the equation  $y=0.4 \sin \left(120\mathrm{\pi } t-\frac{4\mathrm{\pi }}{5} x\right),$ where the distances are given in metre and time in second. Calculate frequency.

A progressive wave in a string is expressed by the equation  $y=0.4 \sin \left(120\mathrm{\pi } t-\frac{4\mathrm{\pi }}{5} x\right),$ where the distances are given in metre and time in second. Calculate wavelength.

The equation of a transverse wave in a string is  $y=1.2 \sin \left(6 t+0.005 x\right) \mathrm{\pi } ,$ where y and x are measured in cm and t in second. Calculate the amplitude, frequency, wavelength and speed of the wave.

The equation of a transverse wave in a string is  $y=1.2 \sin \left(6 t+0.005 x\right) \mathrm{\pi } ,$ where y and x are measured in $\mathrm{cm}$ $t$ in second. Write the equation of that wave whose amplitude and frequency are the same but whose phase difference from the above wave is $+\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.

The equation of motion of a particle is $y=1.2 \sin \left(3.5 t+0.5 x\right)$, where distances and time are respectively in metre and second. Determine the amplitude, frequency and maximum velocity of the particle.