MHTCET 14 May 2023 Shift 1 Solved Paper

As there is no resonant frequency between 315‌Hz and 420‌Hz, let 315‌Hz be n‌th ‌ overtone and 420‌Hz be (n+1)th overtone.
Now, v=‌

nv

2l

....(i)
∴‌‌315=‌

nv

2l

‌ and ‌420=‌

(n+1)v

2l

Taking the ratio,
‌‌

315

420

=‌

n

n+1

∴‌‌315n+315=420n
∴‌‌n=3
The resonant frequency is ν0=‌

v

2l

Therefore, from equation (i) we get,
ν0=‌

ν

n

=‌

315

3

=105‌Hz