An observer standing near the seashore observes 54 waves per minute. If the wavelength of the water wave is 10m then the velocity of a water wave is :

(1) 540 ms^-1

(2) 5.4 ms^-1

(3) 0.184 ms^-1

(4) 9 ms^-1

The equation of a wave is $y=2\sin \pi (0.5x-200t)$, where x and y are expressed in cm and t in sec. The wave velocity is :

1. 100 cm/sec

2. 200 cm/sec

3. 300 cm/sec

4. 400 cm/sec

Equation of a progressive wave is given by

$y=0.2\cos \left(0.04\pi t+0.02\pi x-\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right)$

The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of π/2 :

1. 4 cm

2. 8 cm

3. 25 cm

4. 12.5 cm

Two waves are given by $y_1=a\sin (\omega t-kx)$ and $y_2=a\cos (\omega t-kx)$. The phase difference between the two waves is :

(1) $\frac{\pi }{4}$

(2) π

(3) $\frac{\pi }{8}$

(4) $\frac{\pi }{2}$

If the amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be :

(1) 2A

(2) A

(3) A/2

(4) A/4

A wave is reflected from a rigid support. The change in phase on reflection will be : 

(1) π/4

(2) π/2

(3) π

(4) 2π

A plane wave is represented by $x=1.2\sin (314t+12.56y)$

Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has 

(1) A wavelength of 0.25 m and travels in + ve x-direction

(2) A wavelength of 0.25 m and travels in + ve y-direction

(3) A wavelength of 0.5 m and travels in – ve y-direction

(4) A wavelength of 0.5 m and travels in – ve x-direction

The equation of a wave traveling in a string can be written as $y=3\cos \pi (100t-x)$. Its wavelength is :

(1) 100 cm

(2) 2 cm

(3) 5 cm

(4) None of the above

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. \(y(x,t)=0.5~ \text{cos}(2 \pi x+2\pi t)\)