A closed organ pipe has length l. The air in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a closed organ pipe,the frequencies of harmonics are given by $f_n = (2n-1)f_0$,where $n=1, 2, 3, ...$ corresponds to the fundamental,$1^{st}$

Vedclass · Accepted Answer

$a$

Vedclass · Answer

(B) For a closed organ pipe,the frequencies of harmonics are given by $f_n = (2n-1)f_0$,where $n=1, 2, 3, ...$ corresponds to the fundamental,$1^{st}$ overtone,$2^{nd}$ overtone,and so on.For the $3^{rd}$ overtone,$n=4$,so the frequency is $f_4 = (2(4)-1)f_0 = 7f_0$.The length of the pipe $l$ in terms of wavelength $\lambda$ for the $n^{th}$ harmonic is $l = \frac{(2n-1)\lambda}{4}$.For the $3^{rd}$ overtone $(n=4)$,$l = \frac{7\lambda}{4}$,which implies $\lambda = \frac{4l}{7}$.The displacement amplitude $y(x)$ in a closed organ pipe at a distance $x$ from the closed end (node) is given by $y(x) = a \sin(kx)$,where $k = \frac{2\pi}{\lambda}$.Substituting $k = \frac{2\pi}{(4l/7)} = \frac{7\pi}{2l}$,we get $y(x) = a \sin\left(\frac{7\pi x}{2l}\right)$.At $x = l/7$,the amplitude is $y(l/7) = a \sin\left(\frac{7\pi (l/7)}{2l}\right) = a \sin\left(\frac{\pi}{2}\right) = a(1) = a$.

$A$ closed organ pipe has length $l$. The air in it is vibrating in the $3^{rd}$ overtone with a maximum displacement amplitude $a$. The displacement amplitude at a distance $l/7$ from the closed end of the pipe is:

Similar Questions

If a pipe gives notes of frequencies $375 \ Hz$,$625 \ Hz$,and $875 \ Hz$,what is the fundamental frequency of the pipe and its type?

An open organ pipe of length $L$ vibrates in the second harmonic mode. The pressure vibration is maximum

Two closed pipes produce $10$ beats per second when emitting their fundamental notes. If their lengths are in the ratio of $25 : 26$,then their fundamental frequencies in $Hz$ are:

$A$ pipe open at both ends and a pipe closed at one end have the same length and both are vibrating in their fundamental mode. If the air column vibrating in the open pipe has a resonance frequency $n_1$ and the air column vibrating in the closed pipe has a resonance frequency $n_2$,then:

$A$ closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has

Vedclass Test Series

Exam Paper Generator

Online Exam Module