While walking on the Moon, you cannot hear the sound of stones cracking behind you because:

A wave travelling in the positive x-direction having maximum displacement along y-direction as 1m, wavelength 2π m and frequency of 1/π Hz is represented by

1. y=sin(x-2t)
2. y=sin(2πx-2πt)
3. y=sin(10πx-20πt)
4. y=sin(2πx+2πt)

A transverse wave is represented by y=$A<mspace\; width="1em"></mspace>\sin <mspace\; width="1em"></mspace>\left(\omega t-kx\right).$ For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

(1) $\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{A}/2$                                           

(2) $\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{A}$

(3) $2<mspace\; width="1em"></mspace>\mathrm{\pi }<mspace\; width="1em"></mspace>\mathrm{A}$                                           

(4) A

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) $\lambda =2\pi Y_0$

Which of the following is not possible for sound waves in air?
1. beats
2. interference
3. diffraction
4. polarization

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