Question

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequency of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is ____________.

Options

• 105 Hz

• 1.05 Hz

• 1050 Hz

• 10.5 Hz

Answer 1

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequency of 420 Hz and 315 Hz. There are no other resonant ftequencies between these two. Then, the lowest resonant frequency for this string is 105 Hz.

Explanation:

Let 315 Hz and 420 Hz be n^th and (n + 1)^th harmonics.

`315 = "nv"/(2L)`     ......(i)

`420 = (("n" + 1)"v")/(2L)`   .....(ii)

Dividing (i) by (ii),

`315/420 = "n"/("n"+1) Rightarrow "n" = 3`

`therefore  "Lowest resonant frequency,"`

`f_0 = "v"/(2L) = 315/3 = 105 "Hz"`