Question

You have a pipe that’s open at both ends. With a very precise set of instruments, you discover a resonant frequency at 256 ??. You slowly increase the frequency until you find the next resonance, which occurs at 272 ??. Where could you find the next resonance? A) 280 B) 288 C) 296 D) More than one of these

a. With the same pipe, find the fundamental frequency. A) 16 B) 32 C) 256 D) Not enough info

Answer 1

Given:

Resonant frequency=256 Hz

Next resonant frequency=272 Hz

Formula for calculating resonant frequency of open organ pipe, f_n=nv/2l

where n= 1,2,3...

v=velocity of sound

l=length of organ pipe

f_n​​​​​​=nv/2l=256 .....(1)

f_n+1=(n+1)v/2l=272 ......(2)

Divide equation (2) by equation (1)

(n+1)÷n=272÷256

(n+1)÷n=17÷16

16n+16=17n

n= 16

Put n=16 in equation (1)

16v/2l=256

v/2l=16 ......(3)

next resonant frequency should be at n+2

f_n+2 =(n+2)v/2l

=(16+2)v/2l

=18×16 (since v/2l=16)

=288 Hz

Thus option (B) is correct

Fundamental frequency of open organ pipe=v/2l

=16 Hz

Thus, option (A) is correct