Physics - Chapter 3 #16

Question

A string, stretched between two fixed posts, forms standing wave resonances at 375 HZ and 450 HZ.

What is the greatest possible value of its fundamental frequency?

Answer 1

Both resonance frequencies are multiples of the fundamental frequency, so maximum fundamental is the greatest common divisor of the two frequencies:

375 = 3¹∙5³ Hz

450 = 2¹∙3²∙5²Hz

=>

gcd(375,450) = 3¹∙5² = 75

So maximum fundamental is 75Hz