Tag: standing waves

The length of a stretched string is $2 m$. The tension in it and its mass are $10 N$ and $0.80 kg$ respectively. Arrange the following steps in a sequence to find the third harmonic of transverse wave that can be created in the string.
(a) Find the linear mass density ($m$) using the formula, $m$ $\displaystyle = \dfrac{mass (M)  of \ the \  string}{length (l)  of \ the \  string}$
(b) Collect the data from the problem and find the length($l$) tenstion ($T$) and mass ($M$) of the stretched string.
(c) The fundamental frequency of a stretched vibrating string is given by $n$ $=\displaystyle \dfrac{1}{2l} \sqrt{\dfrac{T}{m}}$
(d) The frequency of $2^{nd}$ overtone or $3^{rd}$ harmonic is given by $n _2\displaystyle = \dfrac{3}{2l}\sqrt{\dfrac{T}{m}}=3n$.

All overtones are stationary wave.

All harmonics in a stringed instrument are

nth overtone and (n/2) harmonic are always equal

All harmonics are possible in a string fixed at one end

A set of 3 standing waves 5, 10 and 15 Hz are to be setup on a string fixed at one end. One of these frequencies are suppressed, while passing through it. Identify them:

The 3rd overtone for a string fixed at one end is 

A medium will not support an infinite number of standing waves of continuously different wavelengths

Find the number of beats produced per sec by the vibrations $x _1=A\sin (320\pi t)$ and $x _2=A\sin (326\pi t)$.

In an organ pipe(may be closed or open) of $99$ cm length standing wave is setup, whose equation is given by longitudinal displacement.
$\xi =(0.1mm)\cos \dfrac{2\pi}{0.8}(y+1cm)\cos 2\pi (400)t$
where y is measured from the top of the tube in meters and t is second. Here $1$cm is the end correction.
The air column is vibrating in :