A transverse wave is represented by the equation   $\mathrm{y} = {\mathrm{y}}_{\mathrm{o}} \sin \frac{2\mathrm{\pi }}{\mathrm{\lambda }} \left(\mathrm{vt} - \mathrm{k}\right)$.  For what value of $\mathrm{\lambda }$ is the particle velocity equal to two times the wave velocity 

• $\mathrm{\lambda } = \mathrm{\pi } {\mathrm{y}}_{\mathrm{o}}$

• $\mathrm{\lambda } = \frac{\mathrm{\pi } {\mathrm{y}}_{\mathrm{o}}}{2}$

• $\mathrm{\lambda } = \frac{\mathrm{\pi } {\mathrm{y}}_{\mathrm{o}}}{3}$

• $\mathrm{\lambda } = 2\mathrm{\pi } \mathrm{i} {\mathrm{y}}_{\mathrm{o}}$

When an open organ is dipped in water upto half of its height, then its frequency will become

• half

• double

• remain same

• four time

43.

A sound source producing waves of frequency 300 Hz and wavelength lm observer is stationary, while source is going away with the velocity 30 m is, then apparent frequency heared by the observer is

• 270 Hz

• 273 Hz

• 383 Hz

• 300Hz

Linear density of a string of is 1.3 x 10^-4 kg/m and wave equation is y = 0.021 sin (x + 30t ), Find, the tension in the string where, x in metre and t in second

• 0.12 N

• 0.21 N

• 1.2 N

• 0.012 N

An observer is approaching with velocity v towards a light source. If the velocity of light is c, then velocity of light with respect to observer will be

• c - v

• c

• c + v

• $\sqrt{1 - \raisebox{1ex}{${\mathrm{v}}^2$}\!\left/ \!\raisebox{-1ex}{${\mathrm{c}}^2$}\right.}$

A 4 kg block is suspended from the ceiling of an elevator through a spring having a linear mass density of 19.2 x 10^-3 kg m^-3 . Find the speed with respect to spring with which a wave pulse can proceed on the spring if the elevator accelerates up at the rate of 2.0 ms^-2.
Take g = 10 ms^-2

• 30 m/s

• 42 m/s

• 46 m/s

• 50 m/s

Figure shows spring + block + pulley system which are light. The time period of mass would be

• $2\mathrm{\pi } \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

• $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

• $\frac{1}{2\mathrm{\pi }} \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

A bat emitting an ultrasonic wave of frequency 4.5 x 10' Hz at speed of 6 m/s between two parallel walls. The two frequencies heared by the bat will be

• 4.67 x 10⁴ Hz, 4.34 x 10⁴ Hz

• 4.34 x 10⁴ Hz, 4.67 x 10⁴ Hz

• 4.5 x 10⁴ Hz, 5.4 x 10⁴ Hz

• 4.67 x 10³ Hz, 4.34 x 10⁴ Hz

A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10³ m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3 %. What is group velocity of the wave packet?

• 0.25 × 10³ m/s

• 1.0 × 10³ m/s

• 0.6 × 10³ m/s

• 0.75 × 10³ m/s

When a stretched wire and a tuning fork are sounded together, 5  beats per second are produced, when length of wire is  95 cm or 100 cm, frequency of the fork is

• 90 Hz

• 100 Hz

• 105 Hz

• 195 Hz