If $\stackrel{\rightharpoonup }{u}$ is the instantaneous velocity of the particle and $\overrightarrow{v}$ is the velocity of the wave, then:

(1) $\stackrel{\rightharpoonup }{u}$ is perpendicular to $\overrightarrow{v}$.

(2) $\stackrel{\rightharpoonup }{u}$ is parallel to $\overrightarrow{v}$.

(3) |$\stackrel{\rightharpoonup }{u}$| is equal to |$\overrightarrow{v}$|.

(4) |$\stackrel{\rightharpoonup }{u}$| = (slope of waveform)x|$\overrightarrow{v}$|.

In a simple harmonic wave, the minimum distance between the particles in the same phase always having the same velocity is:

(1) $\lambda /4$

(2) $\lambda /3$

(3) $\lambda /2$

(4) $\lambda$

The tension in a wire is decreased by 19%. The percentage decrease in frequency will be:

(1) 0.19%

(2) 10%

(3) 19%

(4) 0.9%

On the superposition of the two waves given as:

${\mathrm{y}}_1={\mathrm{A}}_0\sin (\mathrm{\omega t}-\mathrm{kx})$
and ${\mathrm{y}}_2={\mathrm{A}}_0 \cos \left(\mathrm{\omega t}-\mathrm{kx}+\frac{\mathrm{\pi }}{6}\right)$,

the resultant amplitude of oscillations will be:

(1) $\sqrt{3}{A}_0$

(2) $\frac{A_0}{2}$

(3) $A_0$

(4) $\frac{3}{2}{A}_0$

Two waves of amplitudes A₀ and xA₀ pass through a region. If x>1, the difference in the maximum and minimum resultant amplitude possible is:

(1) $(x+1)A_0$

(2) $(x-1)A_0$

(3) $2x{A}_0$

(4) $2A_0$

Which of the following represents a standing wave?

(1) $y=A \sin (\omega t-kx)$

(2) $y=A{e}^{-bx} \sin (\omega t-kx+\alpha )$

(3) $y=A \sin kx \sin (\omega t-\theta )$

(4) $y=(ax+b ) \sin (\omega t-kx)$

The equation of a standing wave in a stretched string is given by $\mathrm{y}=5 \sin \left(\frac{\mathrm{\pi x}}{3}\right) \cos \left(40\mathrm{\pi t}\right)$ where x and y are in cm and t is in seconds. The separation (in cm) between two consecutive nodes is:

(1) 1.5

(2) 3

(3) 6

(4) 4

In a stationary wave:

(1) Strain is maximum at nodes

(2) Strain is minimum at nodes

(3) Strain is maximum at antinodes

(4) Amplitude is zero at all points

In the standing wave shown, the particles at positions A and B have a phase difference of:

(1) 0

(2) $\frac{\pi }{2}$

(3) $\frac{5\pi }{6}$

(4) $\pi$

A 12 m long vibrating string has the speed of wave 48 m/s. To what frequency it will resonate?

(1) 2 cps

(2) 4 cps

(3) 6 cps

(4) All of these