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A person is sitting 200 metres away from a 20- Hz sound source. The time interval at which successive compression pulses from the source reach him is k × 10–2 sec. Where ‘k’ is

Question

A person is sitting 200 metres away from a 20- Hz sound source. The time interval at which successive compression pulses from the source reach him is k × 10–2 sec. Where ‘k’ is

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Solution

The speed of sound in air is approximately 343 m/s.

The frequency of the sound source is given as 20 Hz, which means it produces 20 waves per second.

The wavelength of the sound can be calculated using the formula:

Speed = Frequency x Wavelength

Rearranging for Wavelength gives:

Wavelength = Speed / Frequency

Substituting the given values gives:

Wavelength = 343 m/s / 20 Hz = 17.15 m

The time it takes for one wave to reach the person can be calculated using the formula:

Time = Distance / Speed

Substituting the given values gives:

Time = 200 m / 343 m/s = 0.583 sec

However, this is the time for one wave to travel the distance. The question asks for the time interval between successive compression pulses, which is the same as the period of the wave.

The period of a wave is the reciprocal of its frequency, so:

Period = 1 / Frequency

Substituting the given values gives:

Period = 1 / 20 Hz = 0.05 sec

Therefore, the time interval at which successive compression pulses from the source reach the person is 0.05 sec, or 5 x 10^-2 sec.

So, 'k' is 5.

This problem has been solved

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