A wire of length L and mass per unit length 6.0 × 10^–3 kgm^–1 is put under tension of 540 N. Two consecutive frequencies that it resonates at are : 420 Hz and 490 Hz. Then L in meters is :

Three harmonic waves having equal frequency $$\nu $$ and same intensity $${I_0}$$, have phase angles 0, $${\pi \over 4}$$ and $$ - {\pi \over 4}$$ respectively. When they are superimposed the intensity of the resultant wave is close to :

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 10⁴ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v₀ = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :