Calculate Sound Velocity | Well of 78.4m Depth

Question:

The splash is heard after 4.22 sec after the stone is dropped in to a well of depth 78.4 m.Find the velocity of the sound.

Solution:

Introduction:

The study of speed of sound is crucial for scientific and engineering disciplines in meteorology,it helps in understanding atmospheric conditions and predicting weather patterns.By delving into the principles governing the speed of sound, we can better appreciate its significance and application across various fields.

This understanding not only enriches our knowledge of physical phenomena but also enhances technological advancements that rely on sound propagation.

Calculate the time taken for the stone to fall using equation of motion (t₁):

$${h=\frac{1}{2}gt_1^2}$$

$${t_1=\sqrt\frac{2h}{g}}$$

$${t_1=\sqrt\frac{2(78.4)}{9.8}}$$

$${t_1=\sqrt\frac{156.8}{9.8}}$$

$${t_1=\sqrt{16}}$$

$${t_1=4 \ sec}$$

Time for the sound to travel back up (t₂):

Time taken by the sound to reach top =total time taken(given)-time taken for the stone to fall.

$${t_2 =T-t_1}$$

Time taken by sound to reach the top = 4.22 sec – 4 sec = 0.22 sec.

Velocity of sound:

$${velocity =\frac{78.4}{0.22}}$$

$${velocity =356.36 \ \frac{m}{s}}$$

The velocity of sound is approximately 356.36 ms^-1

Velocity of sound through different media:

Speed of sound -Practical implications

Accurate knowledge of sound speed vital for communication and navigation in aviation.Audio engineers consider it for sound design and acousting treatments.Mateorologist use sound speed data to model atmospheric phenomena.Ultrasound rely on precise measurements of sound speed for medical imaging and treatment purpose.

Conclusion:

Speed of sound in air is well studied physical property with significant theoretical and prctical implications. By mastering the underlying principles and equations, we can enhance our comprehension and application of acoustic phenomena in diverse scientific and engineering domains.