Question

The equation of progressive wave is $Y=4sin\{\pi (\frac{1}{5}-\frac{x}{9})+\frac{\pi }{6}\}$ where x and y are in cm . Which of the following statement is true ?

• A. $\lambda =18cm$
• B. amplitude = 0.04 cm
• C. velocity = 50 cm/s
• D. frequency f = 20 Hz

Answer 1

The correct option is A $\lambda =18cm$

$Y=4\sin (\frac{\pi t}{5}-\frac{\pi x}{9}+\frac{x}{6})$

$Y=A\sin (\cot -4x+\varphi )$

$A=4cm=0.04m$

$k=\frac{\pi }{9}=\frac{2\pi }{\lambda }$

So, $\lambda =18cm$

$f=\frac{2\pi }{\omega }=\frac{2\pi }{\pi /5}=10$

Velcity$=\omega /k=\frac{\pi /5}{\pi /9}=\frac{9}{5}$ cm/sec

So, option (A).