1
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1

A travelling wave is described by the equation

$$y(x,t) = [0.05\sin (8x - 4t)]$$ m

The velocity of the wave is : [all the quantities are in SI unit]

A
$$\mathrm{4~ms^{-1}}$$
B
$$\mathrm{2~ms^{-1}}$$
C
$$\mathrm{8~ms^{-1}}$$
D
$$\mathrm{0.5~ms^{-1}}$$
2
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

In the wave equation

$$y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m}$$

the velocity of the wave will be:

A
200 m/s
B
200$$\sqrt2$$ m/s
C
400 m/s
D
400$$\sqrt2$$ m/s
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

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

A
4$$\pi$$
B
2$$\pi$$
C
$$\pi$$
D
2
4
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Which of the following equations correctly represents a travelling wave having wavelength $$\lambda$$ = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?

A
$$y = A\sin [(0.50\,\pi \,c{m^{ - 1}})x - (100\,\pi \,{s^{ - 1}})t]$$
B
$$y = A\sin \,\,2\pi [(0.25\,\,c{m^{ - 1}})x - (50\,{s^{ - 1}})t]$$
C
$$y = A\sin \left[ {\left( {{{2\pi } \over 4}\,c{m^{ - 1}}} \right)x - \left( {{{2\pi } \over {100}}\,{s^{ - 1}}} \right)t} \right]$$
D
$$y = A\sin \,\pi [(0.5\,\,c{m^{ - 1}})x - (200\,\,{s^{ - 1}})t]$$
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