Question

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.

Answer 1

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 .

Ans:

The winter temperature is .