Question
In: Physics
What is the temperature on the winter day? On a warm summer day (33 ∘C), it...
What is the temperature on the winter day?
On a warm summer day (33 ∘C), it takes 4.70 s for an echo to return from a cliff across a lake. On a winter day, it takes 5.10 s . The speed of sound in air is v≈(331+0.60T)m/s, where T is the temperature in ∘C.
Solutions
Expert Solution
Concepts and reason
The concept used to solve this problem is the change in velocity of sound with the change in temperature.
Use the temperature of a warm summer day to find the distance.
Use the relation of speed of sound and the temperature to find the value of temperature.
Fundamentals
The given expression for the velocity of sound and the temperature is as follows:
Here, 
is the velocity of sound and 
is the temperature of the surrounding.
The expression for speed, distance, and time is as follows:
Here, 
is the distance, speed of sound is 
, and 
is the times.
For summer,
The given expression for the velocity of sound and the temperature is as follows:
Substitute 
for 
.
The expression for speed, distance, and time is as follows:
Substitute 
for 
and 
for 
.
For winter,
The expression for speed, distance, and time is as follows:
Substitute 
for
, 
for 
, and 
for 
.
Rearrange for 
.
The winter temperature is 
.
genius_generous answered 2 years agoRelated Solutions
On a warm summer day (33 ∘C), it takes 4.90 s for an echo to return...
On a warm summer day (33 ∘C), it takes 4.90 s for an echo to
return from a cliff across a lake. On a winter day, it takes 5.30 s
. The speed of sound in air is v≈(331+0.60T)m/s, where T is the
temperature in ∘C.
Part A
What is the temperature on the winter day?
Express your answer to two significant figures and include the
appropriate units.
Tw
Tw
=
∘C
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