Two cars are moving towards each other at the speed of $$50 \mathrm{~ms}^{-1}$$. If one of the cars blows a horn at a frequency of 250 Hz , the wave length of the sound perceived by the driver of the other car is

(Speed of sound in air $$=350 \mathrm{~ms}^{-1}$$)

Speed of sound in air near room temperature is approximately

A body is suspended from a string of length 1 m and mass 2 g. The mass of the body to produce a fundamental mode of 100 Hz frequency in the string is (Acceleration due to gravity $$=10 \mathrm{~ms}^{-2}$$)

Two waves are represented by $$x_1=A \sin \left(\omega t+\frac{\pi}{6}\right) \text { and } x_2=A \cos \omega t \text {. }$$ Then, the phase difference between them is