A wave travelling in the +ve x-direction having maximum displacement along y-direction as 1 m, wavelength $2\pi m$ and frequency of $\frac{1}{\mathrm{\pi }}$ Hz, is represented by:

$1. y=\sin \left(2\pi x-2\pi t\right)$
2. y=sin10πx-20πt
3. y=sin2πx+2πt
4. y=sinx-2t

Two waves are represented by the equations $y_1=a \sin (\omega t+kx+0.57) m$ and $y_2=a\cos (\omega t+kx) m$, where x is in metres and t in seconds. The phase difference between them is:
1. 1.25 rad
2. 1.57 rad
3. 0.57 rad
4. 1.0 rad

A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. $\pi$A/2

2. $\pi$A

3. 2$\pi$A

4. A

A wave in a string has an amplitude of 2 cm. The wave travels in the positive direction of the x-axis with a speed of 128 m/s and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is:

1. y = (0.02)m sin(7.85x+1005t)
2. y = (0.02)m sin(15.7x -2010t)
3. y = (0.02)m sin(15.7x+2010t)
4. y = (0.02)m sin(7.85x -1005t)

The wave described by y = 0.25 sin (10$\pi$x - $2\pi$t), where x and y are in metre and t in second, is a wave travelling along the:

1.  –ve x-direction with frequency 1 Hz

2.  +ve x-direction with frequency π Hz and wavelength $\mathrm{\lambda }$ = 0.2 m

3.  +ve x-direction with frequency 1 Hz and wavelength $\mathrm{\lambda }$ = 0.2m

4.  –ve x-direction with amplitude 0.25 m and wavelength $\mathrm{\lambda }$ = 0.2m

A transverse wave propagating along the x-axis is represented by: 
y(x,t) = 8.0 sin $\left(0.5\mathrm{\pi x}-4\mathrm{\pi t}-\frac{\mathrm{\pi }}{4}\right)$ where x is in meters and t is in seconds. The speed of the wave is:

1. $4\mathrm{\pi } \mathrm{m}/\mathrm{s}$

2. $0.5 m/s$

3. $\frac{\mathrm{\pi }}{4} m/s$

4. $8 m/s$