Two uniform strings A and B made of steel are | vedclass

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

Question

(b) First overtone of string $A$= Second overtone of string $B.$ 

$ \Rightarrow $ Second harmonic of $A$ = Third harmonic of $B$

$ \Rightar

Vedclass · Accepted Answer

$1:3$

Vedclass · Answer

(b) First overtone of string $A$= Second overtone of string $B.$ 

$ \Rightarrow $ Second harmonic of $A$ = Third harmonic of $B$

$ \Rightarrow $ ${n_2} = {n_3}$$ \Rightarrow $ ${\left[ {2({n_1})} ight]_A} = {\left[ {3({n_1})} ight]_B}$ ( $\because$ ${n_1} = \frac{1}{{2l}}\sqrt {\frac{T}{{\pi {r^2}ho }}} $) 

==>$2\,\left[ {\frac{1}{{2{l_A}{r_A}}}\sqrt {\frac{T}{{\pi ho }}} } ight] = 3\,\left[ {\frac{1}{{2{l_B}{r_B}}}\sqrt {\frac{T}{{\pi ho }}} } ight]$ 

$\frac{{{l_A}}}{{{l_B}}} = \frac{2}{3}\frac{{{r_B}}}{{{r_A}}} \Rightarrow \frac{{{l_A}}}{{{l_B}}} = \frac{2}{3} 	imes \frac{{{r_B}}}{{(2{r_B})}} = \frac{1}{3}$

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. if the first overtone of $ A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B,$ the ratio of the lengths of the strings is

Similar Questions

A transverse harmonic wave on a string is described by $y = 3 \sin \,(36t + 0.018x + \frac{\pi}{4})$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two sucessive crests in the wave is .... $m$

Figure, shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ of $1, 2$ and $3$ are in phase with the point $X?$

The length of the string of a musical instrument is $90 \;cm$ and has a fundamental frequency of $120 \;Hz$. Where (In $cm$) should it be pressed to produce fundamental frequency of $180 \;Hz ?$

A tuning fork of frequency $340\, Hz$ is sounded above an organ pipe of length $120\, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is .... $cm$ (speed of sound in air $= 340 \,m/s$)

The length of a sonometer wire tuned to a frequency of $250 Hz$ is $0.60$ metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made $0.40$ metre is .... $Hz$