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Answer:
Answer:
(a)
=
37.
5
T=37.5
o
C
(b)
=
70.09
x=70.09 m
Explanation:
Speed of Sound
The sound travels in an open space at a predictable speed which mainly depends on the air temperature. It can be calculated with an approximate formula in terms of the temperature T in degrees Celsius.
=
331.3
+
0.606
v
s
=331.3+0.606T
The speed comes in m/s
If we have determined the speed of sound, it's possible to estimate the distance to a large obstacle that could cause a returning sound (echo). The formula for the distance is
=
x=v
s
t
Where
v
s
is the speed of sound and t is half the time we hear our echo, because we can measure the forth and back times, assumed to be equal.
(b) We know the air is at -10^oC, so the speed of sound is
=
331.3
+
0.606
(
−
10
)
v
s
=331.3+0.606(−10)
=
325.24
/
v
s
=325.24 m/s
The echo was heard 0.431 seconds later, so t=0.431 / 2= 0.2155 seconds
The distance to the rear wall of the gym is
=
(
325.24
)
(
0.2155
)
x=(325.24)(0.2155)
=
70.09
x=70.09 m
(b) On a summer day, the experiment was repeated and the echo was heard at t = 0.396 seconds. Since we already know the distance to the wall, we can estimate the temperature of the air, by solving the equation for T
=
331.3
+
0.606
v
s
=331.3+0.606T
=
−
331.3
0.606
T=
0.606
v
s
−331.3
We need to compute the new value of
v
s
, with
=
v
s
=
t
x
We know
=
70.09
,
=
0.396
/
2
=
0.198
x=70.09 m,t=0.396/2=0.198 sec
=
70.09
0.198
v
s
=
0.198
70.09
=
354
/
v
s
=354 m/s
Now we can find T
=
354
−
331.3
0.606
T=
0.606
354−331.3
=
22.7
0.606
T=
0.606
22.7
=
37.
5
T=37.5
o
C