A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is

• 2

• 6

• 8

• 7

A uruform wire of length L, diameter D and density ρ is stretched under a tension T. The correct relation between its fundamental frequency f, the length L and the diameter D is

• $\mathrm{f} \propto \frac{1}{\mathrm{LD}}$

• $\mathrm{f} \propto \frac{1}{\mathrm{L}\sqrt{\mathrm{D}}}$

• $\mathrm{f} \propto \frac{1}{{\mathrm{D}}^2}$

• $\mathrm{f} \propto \frac{1}{{\mathrm{LD}}^2}$

The equation of a wave is given by $\mathrm{y} = 10 \sin \left(\frac{2\mathrm{\pi }}{45} \mathrm{t} + \mathrm{\alpha }\right)$. If the displacement is 5 cm at t = 0, then the total phase at t =7.5 s is

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{6}$

• $\mathrm{\pi }$

Two tuning forks A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is

• 250 Hz

• 252 Hz

• 254 Hz

• 256 Hz

A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one-ninth the tension. Then the fundamental frequency will become

• 200 Hz

• 300 Hz

• 600 Hz

• 400 Hz

Wavefront is the locus of all points, where the particles of the medium vibrate with the same

• phase

• amplitude

• frequency

• period

Intensity level of sound whose intensity is 10^-8 Wm^-2 is

• 80 dB

• 8 dB

• 4 dB

• 40 dB

Which ofthe following is incorrect?

• 'Diffraction' helps us to distinguish between sound wave and light wave.

• If the wave is longitudinal, it must be a mechanical wave.

• If the wave is mechanical, it may or may not be a transverse wave

• Mechanical waves cannot propagate in vacuum.

109.

From a fixed support, two small identical spheres are suspended by means of strings of length 1 m each. They are pulled aside as shown and then released. B is the mean position. Then the two spheres collide

                  

• at B after 0.25 s

• at B after 0.5 s

• on the right side of B after some time

• on the right side of B when te strings are inclined at 15° with B

The equation of a transverse wave is given by $\mathrm{y} = 0.05 \sin \mathrm{\pi } \left(2\mathrm{t} - 0.02 \mathrm{x}\right)$, where x, y are in metre and t is in second. The minimum distance of separation between two particles which are in phase and the wave velocity are respectively

• 50 m, 50 ms^-1

• 100 m, 100 ms^-1

• 50 m, 100 ms^-1

• 100 m, 50 ms^-1