In a US household, the voltage in an electric outlet (in volts) is given by the following equation, where t is in seconds.
V = 156sin(120πt)
However, in a European house, the voltage is given (in the same units) by the following equation.
V = 339sin(100πt)

a. How much greater is the maximum voltage in a European house than a US house?
b.What is the number of cycles (oscillations) per second in a US house?

Question

In a US household, the voltage in an electric outlet (in volts) is given by the following equation, where t is in seconds.
V = 156sin(120πt)
However, in a European house, the voltage is given (in the same units) by the following equation.
V = 339sin(100πt) 

a.  How much greater is the maximum voltage in a European house than a US house? 
b.What is the number of cycles (oscillations) per second in a US house?

shane_b · Answer

For part a:  The range of the sine function is from -1 to 1.  So that max for each voltage must be where sin(whatever)=1.  Therefore, the difference would be $$\frac{339}{156}*100=217.31\%$$For part b:  It's 60hz (common knowledge).  I'm not sure how you would calculate that from the info given though.

shane_b · Answer

Also just FYI....it would be 50hz in Europe.