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1. to find the tension, you use the equation: velocity = sqrt(tension/linear density)
you are not given the velocity, but it can be found by: velocity = wavelength x frequency
where the wavelength for a second harmonic is equal to the length of the rope
plug everything in and solve for the tension (make sure all the units match up too)
2. use the same formula as in question 1 to solve for the tension
the linear density can be found by dividing the mass by the length
since it is the "fundamental" harmonic, the wavelength is equal to half the length of the rope
once again, make sure all your units match up
3. for a stationary observer: f ' = f ( Vsound / (Vsound - Vsource))
Vsound is 343m/s and Vsource is the velocity of the fire engine
f is the frequency of the engine and f ' is the frequency hear by the observer
4. W/m^2 is the unit for power where: intensity = power/surface area
the intensity is given and the surface area is 1 m^2
5. for an object completely submerge in water: buoyant force = mass x gravity
the mass can be found by multiplying the density and the volume
make sure your units match up
6. pressure must be conserve and P = F/A so: Fin/Ain = Fout/Aout
pistons are circular so A = pi*r^2 (watch for units again)
you are solving for the amount of force you must apply (Fin) to lift the car (Fout)
7. i'm tired... check the textbook
you are not given the velocity, but it can be found by: velocity = wavelength x frequency
where the wavelength for a second harmonic is equal to the length of the rope
plug everything in and solve for the tension (make sure all the units match up too)
2. use the same formula as in question 1 to solve for the tension
the linear density can be found by dividing the mass by the length
since it is the "fundamental" harmonic, the wavelength is equal to half the length of the rope
once again, make sure all your units match up
3. for a stationary observer: f ' = f ( Vsound / (Vsound - Vsource))
Vsound is 343m/s and Vsource is the velocity of the fire engine
f is the frequency of the engine and f ' is the frequency hear by the observer
4. W/m^2 is the unit for power where: intensity = power/surface area
the intensity is given and the surface area is 1 m^2
5. for an object completely submerge in water: buoyant force = mass x gravity
the mass can be found by multiplying the density and the volume
make sure your units match up
6. pressure must be conserve and P = F/A so: Fin/Ain = Fout/Aout
pistons are circular so A = pi*r^2 (watch for units again)
you are solving for the amount of force you must apply (Fin) to lift the car (Fout)
7. i'm tired... check the textbook