Question 147: Waves

Question

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?

Accepted Answer

We know, equation of wave travelling in positive x-direction is -
$$y = A\sin (kx - wt)$$
where $$k = {{2\pi } \over \lambda }$$
and $$w = 2\pi f$$
Here given $$\lambda$$ = 4 cm and frequency (f) = 100 Hz
$$	herefore$$ $$k = {{2\pi } \over 4} = 0.5\pi $$ cm
$$-$$1
and $$w = 2\pi  	imes 100 = 200\pi $$ s
$$-$$1
$$	herefore$$ Equation of travelling wave,
$$y = A\sin (0.5\pi x - 200\pi t)$$

Answer

$$y = A\sin [(0.50\,\pi \,c{m^{ - 1}})x - (100\,\pi \,{s^{ - 1}})t]$$

Answer

$$y = A\sin \,\,2\pi [(0.25\,\,c{m^{ - 1}})x - (50\,{s^{ - 1}})t]$$

Answer

$$y = A\sin \left[ {\left( {{{2\pi } \over 4}\,c{m^{ - 1}}} \right)x - \left( {{{2\pi } \over {100}}\,{s^{ - 1}}} \right)t} \right]$$

Answer

$$y = A\sin \,\pi [(0.5\,\,c{m^{ - 1}})x - (200\,\,{s^{ - 1}})t]$$

Waves

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?

Choose the correct answer: