Emf on the G string

Electricity and Magnetism Level 4

The fundamental frequency of the G string of a guitar is f=196Hz f= 196 Hz . The fundamental vibrational mode of the string is described by the standing wave y(t,x)=acos⁡(2πft)sin⁡(πxL) y(t,x)= a \cos(2 \pi f t) \sin(\frac{\pi x}{L}) where L=65cmL=65 cm is the length of the string and a=1mm a=1mm is the amplitude of the oscillations. What would be the peak emf in Volts induced across the ends of the string if the guitar is played in a B=2TB= 2T magnetic field?

Assume that the magnetic field is perpendicular to the plane in which the string vibrates.

David Mattingly by David Mattingly
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