A wire fixed at both its ends is found to vibrate at resonant frequencies of 240 Hz and 320 Hz . What could be the maximum value of the fundamental frequency?

Step-by-step solution

For a wire fixed at both ends, the resonant frequencies are given by f_n = n f₀ , where n is an integer and f₀ is the fundamental frequency. The given resonant frequencies are 240 Hz and 320 Hz . Let n₁ f₀ = 240 and n₂ f₀ = 320 for some integers n₁ and n₂ . This implies that f₀ must be a common divisor of 240 and 320 . The maximum value of the fundamental frequency is the greatest common divisor (GCD) of 240 and 320 . GCD (240, 320) = 80 Thus, the maximum possible fundamental frequency is 80 Hz .