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

The difference between the fundamental frequencies of an open pipe and a closed pipe of same length is 100 Hz . The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is

The displacement equations of sound waves produced by two sources are given by $y_1=5 \sin 400 \pi t$ and $y_2=8 \sin 408 \pi t$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is