The tension applied to a metal wire of one metre length produces an elastic strain of $1 \%$. The density of the metal is $8000 \mathrm{kgm}^{-3}$ and Young's modulus of the metal is $2 \times 10^{11} \mathrm{Nm}^{-2}$. The fundamental frequency of the transverse waves in the metal wire is

The path difference between two particles of a sound wave is 50 cm and the phase difference between them is $1.8 \pi$. If the speed of sound in air is $340 \mathrm{~ms}^{-1}$, the frequency of the sound wave is

A source at rest emits sound waves of frequency 102 Hz . Two observers are moving away from the source of sound in opposite directions each with a speed of $10 \%$ of the speed of sound. The ratio of the frequencies of sound heard by the observes is