For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)

Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:

1. $\frac{2u}{\lambda }$

2. $\frac{u}{\lambda }$

3. $\sqrt{\mu \lambda }$

4. $\frac{\mu }{2\lambda }$

The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + $\alpha$), where δ = $\alpha$ + $\pi$/2, then the resultant wave can be represented by:

1. a circle (c.w)

2. a circle (a.c.w)

3. an ellipse (c.w)

4. an ellipse (a.c.w)

If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become:

1. $\frac{n}{4}$

2.  $\sqrt{2}$ $n$ $$

3.  n 

4.  $\frac{n}{\sqrt{2}}$

Two waves have the following equations:

$x_1$ $=$ $a$ $\sin$ $(\omega t$ $+$ ${\varphi }_1)$
$x_2$ $=$ $a$ $\sin$ $(\omega t$ $+$ ${\varphi }_2)$

If in the resultant wave, the frequency and amplitude remain equal to the amplitude of superimposing waves, then the phase difference between them will be:

1.  $\frac{\mathrm{\pi }}{6}$

2. $\frac{2\mathrm{\pi }}{3}$

3. $\frac{\mathrm{\pi }}{4}$

4. $\frac{\mathrm{\pi }}{3}$

If the equation of a wave is represented by: \(y=10^{-4}~ \mathrm{sin}\left(100t-\dfrac{x}{10}\right)~\text m,\) where \(x \) is in meters and \(t\) in seconds, then the velocity of the wave will be: