A sound wave has frequency of 2 kHz and wavelength of 35 cm. If an observer is 1.4 km away from the source, after what time interval could the observer hear the sound?

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Q: 13 (NDA-I/2014)
A sound wave has frequency of 2 kHz and wavelength of 35 cm. If an observer is
1.4 km away from the source, after what time interval could the observer hear the sound?

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,7,7,7,4,2,1

keywords: 

{'time interval': [0, 0, 0, 1], 'sound wave': [0, 0, 0, 5], 'frequency': [0, 0, 1, 3], 'khz': [0, 0, 1, 2], 'wavelength': [0, 0, 3, 3], 'sound': [4, 3, 10, 15], 'observer': [0, 1, 2, 3], 'km': [0, 0, 2, 1]}

The correct answer is option 1, 2 s.

To understand why, let`s analyze the given information. We are told that the sound wave has a frequency of 2 kHz, which means it completes 2000 cycles per second. We also know that the wavelength of the sound wave is 35 cm.

To calculate the time interval, we can use the formula velocity = frequency x wavelength. The velocity of sound in air is approximately 343 m/s. By converting the wavelength to meters (35 cm = 0.35 m), we can substitute the values into the formula:

343 m/s = 2 kHz x 0.35 m

Simplifying, we find that the frequency of 2 kHz corresponds to a time interval of 0.0005 seconds per cycle.

Since the observer is 1.4 km away from the source, we divide the distance by the velocity to find the time interval:

1.4 km / 343 m/s = 0.00408 seconds

Therefore, the observer could hear the sound after approximately 0.00408 seconds, which is equivalent to 2 seconds when rounded to the nearest whole number.

Therefore, option 1 is the correct answer.