An observer is riding on a bicycle and moving towards a hill at $$18 \,\mathrm{kmh}^{-1}$$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $$640 \mathrm{~Hz}$$ and velocity of the sound in air is $$320 \mathrm{~m} / \mathrm{s}$$, the beat frequency between the two sounds heard by observer will be _____________ $$\mathrm{Hz}$$.

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh^$$-$$1 in the direction of wind which is blowing at 72 kmh^$$-$$1 speed. Frequency of siren is 720 Hz. The employee hears an apparent frequency of ____________ Hz.

(Assume speed of sound to be 340 ms^$$-$$1)

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^$$-$$1. The third resonance is observed when the air column has a length of _____________ cm.

A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ___________ cm.

(Velocity of sound in air is 340 ms^$$-$$1)