Question

4. The splash of sound was heard 3.35s after dropping a stone into a well 122.5m deep. Velocity of sound in air is

1) 350 cm/s 2) 350 m/s 3) 392 cm/s 4) 0 cm/s

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Answer 1

᯽QUESTION᯽

The splash of sound was heard 5.35 s after dropping a stone into a well 122.5 m deep. Velocity of sound in air is

✪ᴀɴsᴡᴇʀ✪

• Velocity of sound is $350\:m/s$

★ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ★

Here,

❥︎Total time taken, T = 5.35s

❥︎Depth of well, s = 122.5 m

❥︎Initial velocity of stone, u = 0

❥︎Acceleration of stone,

$\:\:\:\:a = g = 9.8m{s}^{-2}$

❥︎Velocity of sound, $v_s =?$

ᴛɪᴍᴇ ᴏғ ғᴀʟʟɪɴɢ

Applying equation of motion

$\:\:\:\:\:\:\:\:\:\:s = ut + \frac{1 }{2}a{t}^{2}$

$\implies 122.5 = 0 + \frac{9.8}{2}{t}^{2}$

$\implies \frac{122.5\times 2}{9.8} = {t}^{2}$

$\implies \frac{245}{9.8} = {t}^{2}$

$\implies 25 = {t}^{2}$

$\implies t = 5 sec$

Time taken by the stone in reaching the water is 5 sec.

Velocity ᴏғ sᴏᴜɴᴅ

Time taken by sound to travel from bottom of well to the top

$t_s = T - t = 5.35-5 = 0.35\:s$

Velocity of sound is given by

$\implies v_s = \frac{s}{t_s}$

$\implies v_s = \frac{122.5\:m}{0.35\:}$

$\implies v_s = 350\:m/s$

Velocity of sound is 350 m/s.