Two strings of the same material are stretched to the same tension. If their radii are in the ratio of 1: 2, then respective wave velocities in them will be in the ratio of:

(1) 4: 1

(2) 2: 1

(3) 1: 2

(4) 1: 4

A pulse is generated at the lower end of a hanging rope of uniform density and length L. The speed of the pulse when it reaches the midpoint of the rope is:

(1) $\sqrt{2gL}$

(2) $\sqrt{gL}$

(3) $\sqrt{\frac{gL}{2}}$

(4) $\frac{\sqrt{gL}}{2}$

The sound intensity level at a point 4 m from the point source is 10 dB. Then the sound level at a distance of 2 m from the same source will be:

(1) 26 dB

(2) 16 dB

(3) 23 dB

(4) 32 dB

The tones that are separated by three octaves have a frequency ratio of:

(1) 3

(2) 6

(3) 8

(4) 16

A wave is represented by $x=4\cos \left(8t-\frac{y}{2}\right)$, where x and y are in metres and t in seconds. The frequency of the wave (in sec^-1) is:

(1) $\frac{4}{\pi }$

(2) $\frac{8}{\pi }$

(3) $\frac{2}{\pi }$

(4) $\frac{\pi }{4}$

A wave is represented by the equation

$\mathrm{y}=\mathrm{Asin}\left(10\mathrm{\pi x}+15\mathrm{\pi t}+\frac{\mathrm{\pi }}{6}\right)$

where x is in metres and t in seconds. The expression represents:

(1) a wave travelling in the negative x-direction with a velocity of 1.5 m/s.

(2) a wave travelling in the positive x-direction with a velocity of 1.5 m/s.

(3) a wave travelling in the positive x-direction with wavelength 0.2 m.

(4) a wave travelling in the negative x-direction with a velocity of 150 m/s.

A travelling wave in a string is represented by $y=3\sin \left(\frac{\pi }{2}t-\frac{\pi }{4}x\right)$. The phase difference between two particles separated by a distance of 4 cm is:

(Take x and y in cm and t in seconds)

(1) $\frac{\pi }{2}$ rad

(2) $\frac{\pi }{4}$ rad

(3) $\pi$ rad

(4) 0

A transverse wave is described by the equation $\mathrm{y}=\mathrm{Asin}2\mathrm{\pi }\left(\mathrm{nt}-\mathrm{x}/{\mathrm{\lambda }}_0\right)$. The maximum particle velocity is equal to 3 times the wave velocity if:

(1) ${\lambda }_0=\frac{\pi A}{3}$

(2) ${\lambda }_0=\frac{2\pi A}{3}$

(3) ${\lambda }_0=\pi A$

(4) ${\lambda }_0=3\pi A$

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|$\overrightarrow{v}$|.