# Distance of building related to echo

## Homework Statement

A road lies between two parallel buildings. A motorist travels with speed 36 km/h on the road and hits the horn. He heard the echo 1 second later. The speed of sound is 330 m/s
a. Find the distance of the building
b. When will he hear the second echo?

2d = v.t

## The Attempt at a Solution

The first echo will come from the nearest building and the second echo will come from the further building.

a. the distance of nearest building to motorist = d1
2 d1 = v.t
d1 = 115 m

I don't know how to find the distance of further building to the motorist and is the speed of motorist being used in the calculation?

Thanks

## Answers and Replies

Related Introductory Physics Homework Help News on Phys.org
ehild
Homework Helper

## Homework Statement

A road lies between two parallel buildings. A motorist travels with speed 36 km/h on the road and hits the horn. He heard the echo 1 second later. The speed of sound is 330 m/s
a. Find the distance of the building
b. When will he hear the second echo?

2d = v.t

## The Attempt at a Solution

The first echo will come from the nearest building and the second echo will come from the further building.

a. the distance of nearest building to motorist = d1
2 d1 = v.t
d1 = 115 m

I don't know how to find the distance of further building to the motorist and is the speed of motorist being used in the calculation?

Thanks
Try to imagine you are the motorist, travelling on the road in between two parallel buildings. What do you mean on "nearest" and "further" building? Show the path of the sound that hits the ears of the motorist in a figure.

ehild

Try to imagine you are the motorist, travelling on the road in between two parallel buildings. What do you mean on "nearest" and "further" building? Show the path of the sound that hits the ears of the motorist in a figure.

ehild

Let P be the motorist and there are two parallel buildings on his right and left side. The nearest building is the right one and the further building is the left one. The motorist moves "into the page" with respect to the reader (same as (×) sign of magnetic field)

The sound will hit the right building first and being reflected to his ear. Sound will also be reflected by the left building and he will hear the second echo.

But I don't know how to calculate the distance...

NascentOxygen
Staff Emeritus
I'd say the intention is that the road follows a path exactly midway between the buildings.

I'd say the intention is that the road follows a path exactly midway between the buildings.
Oh I see, the distance is twice of what I've calculated. So the speed of the motorist is not important?

Thanks

NascentOxygen
Staff Emeritus
Oh I see, the distance is twice of what I've calculated. So the speed of the motorist is not important?

Thanks
The motorist will be in a different location each time an echo reaches his ears, so I'd say you do have to take into account his movement. I'm picturing it as the motorist in an open-top sports car reaching up and firing a starter's pistol as he passes between the buildings (or as he drives through a canyon with steep sides). How long before the radiating pressure wave gets back to him in some form?

The motorist will be in a different location each time an echo reaches his ears, so I'd say you do have to take into account his movement. I'm picturing it as the motorist in an open-top sports car reaching up and firing a starter's pistol as he passes between the buildings (or as he drives through a canyon with steep sides). How long before the radiating pressure wave gets back to him in some form?
I am not sure, maybe 1 second because that is the time needed for him to hear an echo.

ehild
Homework Helper
To make easier to imagine, see picture. The motorist drives just in the middle of the road between the pair of long buildings, at distance D from both, with speed V=36 km/h. He hits the horn: the sound travels in every direction and reaching the wall of the buildings, reflects. A narrow beam of sound wave reaches the middle of the road just as the motorist also reaches there, Δt=1 s later as the horn was hit. The motorist travelled S=VΔt distance. How long distance travelled the sound during that time if the speed of sound is 330 m/s? The path of the sound and that of the motorist make an isosceles triangle. What is D then?

ehild

#### Attachments

• 15.6 KB Views: 261
Last edited:
The distance travelled by the motorist in interval 1 s = 10 m
The distance travelled by the sound in interval 1 s = 330 m

D = √(52 + 1652) = 165.076 m

a. distance between building = 2D

b. he will hear the second echo 1 s later ??

Thanks

ehild
Homework Helper
The distance travelled by the motorist in interval 1 s = 10 m
The distance travelled by the sound in interval 1 s = 330 m

D = √(52 + 1652) = 165.076 m

a. distance between building = 2D

b. he will hear the second echo 1 s later ??

Thanks
Check it. Is D the hypotenuse?

ehild

Check it. Is D the hypotenuse?

ehild
Oh yes, I see my mistake.

For answer (b), am I correct? I think the answer will be 1 s because the motorist and sound undergo uniform motion

ehild
Homework Helper
Yes, of course, the second echo follows the first one after 1 s.

ehild

Yes, of course, the second echo follows the first one after 1 s.

ehild
Thanks for the help