In a stretched string:

(1) Only transverse waves can exist

(2) Only longitudinal waves can exist

(3) Both transverse and longitudinal waves can exist

(4) None of these

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) ${\lambda }_0=3\pi A$