Question 505: Waves

Question

A transverse wave is represented by 
y = Asin($$\omega $$t $$-$$ kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?

Accepted Answer

y = A sin ($$\omega $$tÃ¢ÂÂkx)
Particle velocity,
$${v_p} = {{dy} \over {dt}} = A\omega \cos \left( {\omega t - kx} ight)$$
$$ 	herefore {v_{p\,\max }} = A\omega $$
wave velocity = $${\omega  \over k}$$
$$ 	herefore $$ $$A\omega  = {\omega  \over k}$$
i.e, $$A = {1 \over k}$$ But $$k = {{2\pi } \over \lambda }$$
$$ 	herefore \lambda  = 2\pi A$$

Answer

$$\pi A/2$$

Answer

$$\pi A$$

Answer

2$$\pi A$$

Answer

$$A$$

Waves

A transverse wave is represented by y = Asin($\omega t -$ kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?

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