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:

A transverse wave is represented by $$y=2 \sin (\omega t-k x)\, \mathrm{cm}$$. The value of wavelength (in $$\mathrm{cm}$$) for which the wave velocity becomes equal to the maximum particle velocity, will be :