Why Do Sound Waves Travel Faster in Steel Than in Air?

AI Thread Summary
Sound waves travel faster in steel than in air due to the material's density and elasticity, with speeds of 5960 m/s in steel and 346 m/s in air. To solve the problem of determining the distance to the man hammering on the track, one should use the formula d = vt for both mediums. Set up equations for the distance traveled by sound in steel and air, noting that the sound in steel arrives 5 seconds earlier. By relating the two distances and eliminating variables, one can solve for the time difference and subsequently find the distance. Understanding these principles is essential for solving similar physics problems effectively.
CanMousePlate
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A man hammers on a steel railway track. If you hear the sound through the track 5.0 seconds sooner than through the air, how far away is the man?
*Steel - 5960m/s
*Air - 346 m/s
The question is simple but i can't get it

Also please explain how to do a question like this in the answer.
 
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Welcome to PF, CanMousePlate!
First, you need to collect the formulas that describe the physics involved.
You did answer d = vt for motion at constant speed, right?
You need to write this twice, once for the high speed waves in the steel and once again for the slower speed in air.
Next, sort out the distances. How are the two d's related? That should eliminate the d's and leave you with only unknown times. The two times are related, put that into your equation so only one unknown left. Solve for that time. Use it in the appropriate one of your d = vt equations to find the distance.
 
CanMousePlate said:
A man hammers on a steel railway track. If you hear the sound through the track 5.0 seconds sooner than through the air, how far away is the man?
*Steel - 5960m/s
*Air - 346 m/s
The question is simple but i can't get it

Also please explain how to do a question like this in the answer.

Welcome to the PF.

You must try to solve the question on your own here before asking for our help. Please check your PMs. You received a reminder of the PF rules that you agreed to when joining here.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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