QJEEM23Phb44d: JEE Main 2023 Physics - Class 11 JEEM23Phb44d Solution: The equation of wave is given by where and are in and in . The…

Given the wave equation:

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

Comparing this equation with the general form:

$Y = A \sin(2\pi(ft - kx + \phi))$

We can identify the wave number $k = 0.5\,\mathrm{m}^{-1}$ and the frequency $f = 160\,\mathrm{Hz}$ . The wave speed $v$ can be found using the relationship between wave number, wave speed, and frequency:

$v = \frac{\omega}{k} = \frac{2\pi f}{2\pi k}$

Now, we can calculate the wave speed:

$v = \frac{2\pi \times 160}{2\pi \times 0.5} = \frac{160}{0.5}\,\mathrm{m/s}$

$v = 320\,\mathrm{m/s}$

Now, we need to convert the wave speed from meters per second to kilometers per hour:

$v = 320 \frac{\mathrm{m}}{\mathrm{s}} \times \frac{1\,\mathrm{km}}{1000\,\mathrm{m}} \times \frac{3600\,\mathrm{s}}{1\,\mathrm{h}}$

$v = 320 \times \frac{1}{1000} \times 3600\,\mathrm{km/h}$

$v = 1152\,\mathrm{km/h}$

So, the speed of the wave is $1152\,\mathrm{km/h}$ .