Speed of sound minimum distance problem

[bigsaucy]

Hi all, just a question I am having trouble with

1.) You're watching a carpenter pound a nail. He hits the nail twice a second, but you hear the sound of the strike when his hammer is fully raised. What is the minimum distance from you to the carpenter? assume the air temperature is 20 degrees celcius.

I figured that since the speed of sound in air at 20 degrees celcius is 343 m/s and it takes him 0.50 seconds to hit the nail once, that the minimum distance is (0.5) (343) which is 171.5 m but the book says the answer is 86m

 

[SteamKing]

You're not accounting for the fact that although the nail is struck twice in one second, it takes a certain amount of time for the man to raise his hammer for the next strike on the nail head. Look at it this way: time = 0, hammer hits nail; time = 0.25 s, hammer at max. height above nail and you hear sound from previous strike; time = 0.50 s, hammer hits nail, time = 0.75 s, hammer at max. height and sound is heard; time = 1.0 s, hammer hits nail. Therefore, you are 0.25 * 343 = 85.75 m from the nail.

 

[bigsaucy]

ok thanks for that, i understand it now. since you're here I might as well get help with another quesiton:

Oil explorers set off explosives to make louds sounds, then listens for the echoes from underground oil deposits. Geologists suspect that there is oil under 500-m deep lake physics. It's known that lake physics is carved out of a granite basin. Explorers detect a weak echo 0.94s after exploding dynamite at the lake surface. If it's really oil, how deep will they have to drill into the granite to reach it?

i reasoned that since the speed of sound in water is 1480 m/s and it takes 0.94/s or 0.47 seconds to reach the oil bed, that the sound wave from the explosion travels 695.6m which is 195.6m from the granite basin. the book says the answer is 760m

 

[olivermsun]

Do they tell you the speed of sound in granite? It should be much faster than in water, right?

 

[rwisz]

The minimum distance in this problem is determined by the time it takes for sound to travel from the carpenter to you. Since the sound of the strike is heard when the hammer is fully raised, this means that the sound has to travel twice the distance from the carpenter to you.

To calculate the minimum distance, we can use the formula: distance = speed x time. In this case, the speed is the speed of sound in air at 20 degrees Celsius, which is 343 m/s. The time is half a second, since the carpenter hits the nail twice a second but we only hear the sound once.

So the minimum distance would be (343 m/s) x (0.5 s) = 171.5 m. However, this only accounts for one direction of travel. Since the sound has to travel to you and then back to the carpenter, the total distance would be twice this amount, which equals 343 m. This is the minimum distance from you to the carpenter.

It is possible that the book's answer of 86 m is a typo or a mistake. It is important to double check the calculations and make sure all the variables and units are correct. It is also possible that the book is using a different approach to solving the problem. Regardless, the minimum distance should be 343 m based on the given information.