Question

You are camping in Glacier National Park. In the midst of a glacier canyon, you make a loud holler. You hear an echo 1.22 seconds later. A. How far away are the canyon walls if you assume that the speed of sound in air is 343m/s? B. If the temp of the air drops significantly, what would happen to the speed of the sound in the air?

Answer 1

Given,

Speed of sound in air = 343m/s

The body hears echo after 1.22seconds.

=>2t=1.22seconds

(As the sound travels from the mouth of body to the wall and returns back to the body after this the body hears echo.So,In this manner if we consider the time taken by the sound to travel from the body to wall as "t".Then,the time to hear the echo will be "2t" as the sound travels same distance with same speed.)

=>2t = 1.22sec

=>t =0.61sec

By using the formula of speed we can calculate the distance of the wall.

The formula of speed is given by

V= d / t.......(1)

Where,V= speed

d=distance

t= time

From equation 1

d = v×t...........(2)

By putting the value of v and t from question we will get the value of distance of the wall.

So, d = v×t

d = 343m/s×0.61s

d = 343×0.61 (m/s)(s)

d=343×0.61m

d = 209.23m

=> d = 209.23m

=> d = 209m

And let suppose if the temperature (T) of the air drop is significant.

So,the speed of sound will be differ from the given value of sound.

(As sound also a wave and propagation of a wave depends upon the properties of the medium.So, speed of sound will be differ from the given value of sound.)

Let's suppose temperature dependent speed of sound be V​​​​​​1

So,The temperature (T) dependent speed of sound will be equals to the given equation(3)

=> ​​​​​​​V 1 =331 m/s + (0.6 m/s/°C) × T ..........(3)

Summary:-​​​​​​-A).The distance of canyon walls is d =209.23m =209m

B).If the temperature (T) of air drops are significant.Then the speed of sound will be temperature dependent and it can be calculated by the equation (3)

V 1 =331 m/s + (0.6 m/s/°C) × T ..........(3)