Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is .................. Hz.

Two waves are simultaneously passing through a string and their equations are :

y₁ = A₁ sin k(x $$-$$ vt), y₂ = A₂ sin k(x $$-$$ vt + x₀). Given amplitudes A₁ = 12 mm and A₂ = 5 mm, x₀ = 3.5 cm and wave number k = 6.28 cm^$$-$$1. The amplitude of resulting wave will be ................ mm.

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be ............... Hz.

Two travelling waves produces a standing wave represented by equation,

y = 1.0 mm cos(1.57 cm^$$-$$1) x sin(78.5 s^$$-$$1)t.

The node closest to the origin in the region x > 0 will be at x = .............. cm.