ECHO...ECHo...ECho...Echo...echo...

The Grand Canyon is anywhere from 6 6 to 30 km 30~\mbox{km} across. If you stood on one side of the Grand Canyon at its narrowest point and shouted, how long in seconds would it take for you to hear your echo?

Details and assumptions

  • The speed of sound is roughly 350 m/s 350~\mbox{m/s} .


The answer is 34.29.

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12 solutions

Russell Few
Sep 16, 2013

The distance for the sound to travel is ( 6 k m ) ( 2 ) = 12 k m = 12000 m (6km)(2)=12km=12000m . The echo would take 12000 m 350 m s = 34.29 \frac{12000m}{350\frac{m}{s}}=\boxed{34.29} seconds.

Alexander Sludds
Dec 17, 2013

At the narrowest point the distance that the sound has to travel is equal to 12KM because the sound has to return. Thus, we can calculate the amount of seconds that sound has to travel for as 12000m*1s/350m=34.290s

I don't really understand the question. If you're standing in the middle then the sound has to travel 3 meters there and 3 back. But if you're standing at the edge of the wall the sound has to travel 0 meters.

Aradhya Kasera - 7 years, 5 months ago

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The question says "If you stood on one side ... how long would it take you to hear your echo. " The phrase "your echo" specifically implies that the sound bounces off the other side of the Canyon and then comes back to you.

Michael Tang - 7 years, 5 months ago

so suppose the grand canyon's distance is 30 Km, then the answer would be 171.43s?

Ela Cordero - 7 years, 5 months ago

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ofcourse.....

Abdul Muiz - 7 years, 5 months ago

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Thank you.

Ela Cordero - 7 years, 5 months ago

why the distance be 6km?????? it's said it can be any where b/w 6-30

Akash Kumar - 7 years, 5 months ago

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because it will the first echo you hear, you know, just let's say the nearest canyon

Edward Jeremy Lo - 7 years, 3 months ago

What if the distance was 30 km? At first I calculated for 30 and got it wrong .

Sharath Chandar - 7 years, 5 months ago

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Actually the problem says: "at its narrowest point" explaining that the minimum distance (6km) should be used.

Jose Reinaldo - 7 years, 5 months ago

I used 15 km as distance.then 15000*2=30000/350=85.7.why is it wrong?

Sanjay Balaji - 7 years, 2 months ago
Nicholas Wei
Dec 18, 2013

Narrowest point = 6 km.

For echo to reach other end and come back to you, total distance travelled by sound = 6km x 2 = 12 km

Time taken for echo to reach back to you = 12000m (distance travelled)/ 350m/s (speed of sound) = 34.29s (to 4sf)

Akshat Prakash
Sep 16, 2013

velocity(v)=displacement(s)/time(t)

By rearranging we get,

t = s/v

(Putting in values)

s = 12 km (counting both ways) = 12,000m

v = 350m/s (given)

t =6 2 1000/350=34.29

but the question asked that the canyon is between 6&30 not exactly at 6 km so how can you assume 6km as a distance..

Harsh Dubey - 7 years, 8 months ago

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It says in the question-" at it's narrowest points " which is as given 6km

Akshat Prakash - 7 years, 8 months ago
Yao Feng Ooi
Dec 29, 2013

(6000*2)/350=34.285

Shivam Gulati
Sep 20, 2013

The distance for the sound to travel is (6km)(2)=12km=12000m. The echo would take 12000m350ms=34.29 seconds.

Well the solution is correct, but it resembles Russell F.'s solution word by word except for the LaTex edits. You could have written it out in your own words.

Nishant Sharma - 7 years, 7 months ago

for this problem, the narrowest point would be 6 km or 6,000 m, the speed of sound is roughly 350 m/s

so we can use the formula t = s v \frac {s}{v}

thus we will obtain t = 6000 350 \frac {6000}{350}

that is equal to 17.142857 and so on but it is the time for the sound to reach the end of 6km cliff , so to obtain the total time until we hear the echo

17.142857 × 2 17.142857 \times 2 = 34.285714

and by using decimal approach we will obtain 34.3 \boxed {34.3}

Nitish Dubey
Jan 18, 2014
  • As we are standing at the narrowest point therefore, the distance that we have to take is 6 Km.
  • Now,the distance to be travelled by the sound is = 2 × 6000 2 \times 6000 m.
  • Hence the net Time = 12000/350 sec. = 34.3 sec
Fienny Angelina
Dec 27, 2013

You stood at its narrowest point, therefore, you are 6 km in distance. You shouted, the sound will travel to the place, and then bounce back to your ears so you can hear the echo. Therefore, it travels 12 km, or 12000meters. From the details above, you can see that the speed of sound is considerably 350 m/s. And we know that s = v.t Where s = the distance travelled by the sound which is 12000m and v is the velocity of the sound, which is 350 m/s, so by putting these quantity in the above equations, the time taken would be 34.290 s

Saqib M
Dec 26, 2013

The question says the we are on a side of a narrowest point, so the other end would be 6 KM away. My echo would have to travel 6+6=12 KM(the sound wave has to go and return also). So, the distance is 12,000 Meters and speed is 350 m/s. Therefore, Time taken= 12000/350 = 34.285 seconds

Emma Unsworth
Dec 22, 2013

Total distance travelled is twice the diameter, therefore 6km x 2

Divided by the speed of sound 350, which is (12000(m)/350(m/s)) = 34.2857... s.

Aniket Sen
Dec 18, 2013

Easy, The narrowest corner is 6KMs. The sound needs to travel 6 2 (upstream & downstream) = 12 KMs...speed of sound is 350m/s...hence the solution is 12 1000/350 = 34.290

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