Question

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

• A. $\lambda =18cm$
• B. $Amplitude=0.04cm$
• C. $velocityv=50cm/s$
• D. $frequencyf=20Hz$

Answer 1

Answer: (A)

$\lambda =18cm$

The general equation of progressive wave,

$Y=Asin(wt-kx+\varphi )$ . . . . .(1)

Given,

$Y=4sin\left[\pi (\frac{t}{5}-\frac{x}{9}\right)+\frac{\pi }{6}]$. . . . .(2)

Comparing equation (1) and (2), we get

$w=\frac{\pi }{5}$, $k=\frac{\pi }{9}$, $\varphi =\frac{\pi }{6}$

Amplitude $A=4cm$

we know that, propagation constant,

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

$\lambda =18cm$

Velocity, $v=\frac{w}{k}$

$v=1.8cm/s$

And the frequency

$f=\frac{1}{2\pi w}=\frac{1}{2\pi \times \frac{\pi }{5}}$,

$f=2.5Hz$

From above the correct option is A.