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(A) The wave speed $v$ is given by $v = \frac{	ext{distance}}{	ext{time}} = \frac{1.2 \ cm}{0.3 \ s} = 4 \ cm/s$.The angular wave number $k$ is $k =

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$y = 2 \cos (0.83 x - 3.35 t) \ cm$

Vedclass · Answer

(A) The wave speed $v$ is given by $v = \frac{	ext{distance}}{	ext{time}} = \frac{1.2 \ cm}{0.3 \ s} = 4 \ cm/s$.The angular wave number $k$ is $k = \frac{2 \pi}{\lambda} = \frac{2 \pi}{7.5 \ cm} \approx 0.837 \ rad/cm \approx 0.83 \ rad/cm$.The angular frequency $\omega$ is $\omega = v k = 4 \ cm/s 	imes 0.837 \ rad/cm \approx 3.35 \ rad/s$.Since the crest is at $x = 0$ at $t = 0$,the wave is represented by a cosine function: $y = A \cos(kx - \omega t)$.Substituting the values,$y = 2 \cos(0.83 x - 3.35 t) \ cm$.

$A$ sinusoidal wave of wavelength $7.5 \ cm$ travels a distance of $1.2 \ cm$ along the $x$-direction in $0.3 \ s$. The crest $P$ is at $x = 0$ at $t = 0 \ s$ and the maximum displacement of the wave is $2 \ cm$. Which equation correctly represents this wave?

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