A steel wire with mass per unit length $$7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$$ is under tension of $$70 \mathrm{~N}$$. The speed of transverse waves in the wire will be:

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $$30 \mathrm{~m} / \mathrm{s}$$. If both trains emit sounds with frequency $$300 \mathrm{~Hz}$$, (Speed of sound: $$330 \mathrm{~m} / \mathrm{s}$$) approximate difference of frequencies heard by the person will be:

A travelling wave is described by the equation

$$y(x,t) = [0.05\sin (8x - 4t)]$$ m

The velocity of the wave is : [all the quantities are in SI unit]

In the wave equation

$$ y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m} $$

the velocity of the wave will be: