A transverse wave is described by the equation $y=Y_0\sin \left(2\mathrm{\pi ft}-\frac{2\mathrm{\pi }}{\mathrm{\lambda }}\mathrm{x}\right)$. The maximum particle velocity is four times the wave velocity if :

(1) $\lambda =\frac{\pi Y_0}{4}$

(2) $\lambda =\frac{\pi Y_0}{2}$

(3) $\lambda =\pi Y_0$

(4) $\lambda =2\pi Y_0$

A transverse wave with an amplitude of \(0.5\) m, a wavelength of \(1\) m, and a frequency of \(2\) Hz is propagating along a string in the negative \(x\)-direction. The expression for this wave is:
1. \(y(x,t)=0.5~ \text{sin}(2 \pi x-4\pi t)\)
2. \(y(x,t)=0.5~ \text{cos}(2 \pi x+4\pi t)\)
3. \(y(x,t)=0.5~ \text{sin}( \pi x-2\pi t)\)
4. \(y(x,t)=0.5~ \text{cos}(2 \pi x+2\pi t)\)

Which one of the following does not represent a traveling wave :

1. $y=\sin (x-vt)$

2. $y=y_m\sin k(x+vt)$

3. $y=y_m\sin (x-vt)$

4. $y=f(x^2-v{t}^2)$

A transverse wave is represented by the equation $y=y_0\sin \frac{2\pi }{\lambda }(vt-x)$

For what value of λ, the maximum particle velocity equal to two times the wave velocity?

(1) $\lambda =2\pi y_0$

(2) $\lambda =\pi y_0/3$

(3) $\lambda =\pi y_0/2$

(4) $\lambda =\pi y_0$

A wave travels in a medium according to the equation of displacement given by $y(x,t)=0.03\sin \pi (2t-0.01x)$ where y and x are in metres and t in seconds. The wavelength of the wave is :

1. 200 m

2. 100 m

3. 20 m

4. 10 m

The frequency of the sinusoidal wave $y=0.40\cos [2000t+0.80x]$ would be :

(1) 1000 π Hz

(2) 2000 Hz

(3) 20 Hz

(4) $\frac{1000}{\pi }Hz$

The equation of a plane progressive wave is given by $y=0.025\sin (100t+0.25x)$. The frequency of this wave would be :

(1) $\frac{50}{\pi }Hz$

(2) $\frac{100}{\pi }Hz$

(3) 100 Hz

(4) 50 Hz