Posted by Anonymous on .
A stretched wire vibrates in its fundamental mode at a frequency of 420 Hz. What would be the fundamental frequency if the wire were one fourth as long, its diameter were quadrupled, and its tension were increased twofold?

physics 
drwls,
With 4 times the diameter (and assuming the same material density), the mass per unit length would increase by a factor of 16. The ratio (tension)/(linear density) would be 2/16 = 1/8 of its previous value. The wave speed is proportional to the square root of that, or 0.3536 as large as before.
The fundamental frequency is proportional to (wave speed)/(length). This changes by a factor 0.3536/0.250 = 1.414
The new fundamential frequency is 594 Hz.