Two identical strings X and Z made of same material have tension T_X and T_Z in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio T_X/T_Z is

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 :