Question

ᴀ ᴍᴀɴ sᴛᴀɴᴅɪɴɢ ʙᴇᴛᴡᴇᴇɴ ᴛᴡᴏ ᴠᴇʀᴛɪᴄᴀʟ ᴡᴀʟʟs 680ᴍ ᴀᴘᴀʀᴛ.ʜᴇ ᴄʟᴀᴘs ʜɪs ʜᴀɴᴅs ᴀɴᴅ ʜᴇᴀʀs ᴛᴡᴏ ᴅɪsᴛᴀɴᴛ ᴇᴄʜᴏᴇs 0.9 sᴇᴄᴏɴᴅs ᴀɴᴅ 1.1 sᴇᴄᴏɴᴅ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ .ᴡʜᴀᴛ ɪs ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ sᴏᴜɴᴅ ɪɴ ᴛʜᴇ ᴀɪʀ​

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Answer 1

$\rm the \:man \:is \:not\: situated\: exactly$

$\rm between \:the \:two\: walls$

$\tt let\:he\:be\:x\:metres\:away\:from$

$\tt the\:first\:wall$

$\tt =>y = distance\:from\:2nd\:wall$

$\boxed{\tt =>x+y=680}$...............(1)

distance travelled by the sound

$\tt =2x+2y$

when he claps,

the sound travels 2x+2y distance to reach the man back.

•we know that speed of sound Is a constant.

•time to hear the 2 echoes are 0.9 and 1.1 respectively.

•we can form an equation as

$\tt \dfrac{2x}{0.9}=\dfrac{2y}{1.1}$

$\tt 2.2x = 1.8y$

$\tt 2.2x-1.8y=0$.............. (2)

solving equations 1 and 2,

the values of x and y will come as:

$\boxed{\tt y=376.75}$

$\boxed{\tt x=308.25}$

placing this value of x in equation 2,

speed of air = 2x/0.9

= 680m/s

so half the speed = 340m/s

since the air travels distance to and fro, we divide it by 2..

hence your answer is 340m/s

Answer 2

Let speed of sound be v

2x/ v = 0.9

2(680-x)/v = 1.1

2v = 1360

v = 1360/2

v = 680 m/s