A string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be
Medium
Download our app for free and get started
$\frac{{{{\rm{f}}_T}}}{{{{\rm{f}}_\ell }}} = \sqrt {\frac{{\frac{{\rm{T}}}{\mu }}}{{\frac{{\rm{r}}}{{\rm{s}}}}}} = \sqrt {\frac{{\frac{{\rm{T}}}{{\rho {\rm{A}}}}}}{{\frac{{{\rm{T}}\ell }}{{\rho {\rm{A}}\Delta \ell }}}}} = \sqrt {\frac{{\Delta \ell }}{\ell }} = \frac{1}{{\sqrt \eta }}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The speed of a wave in a certain medium is $960\, m/s$. If $3600$ waves pass over a certain point of the medium in $1\, minute$, the wavelength is .... $metres$View Solution
- 2View SolutionWhen temperature increases, the frequency of a tuning fork
- 3A wave has velocity $u$ in medium $P$ and velocity $2u$ in medium $Q.$ If the wave is incident in medium $P$ at an angle of $30°$ then the angle of refraction will be .... $^o$View Solution
- 4Two small identical speakers are connected in phase to the same source. The speakers are $3 \,m$ apart and at ear level. An observer stands at $P, 4 \,m$ in front of one speaker as shown alongside. The sound she hears is least intense when the wavelength is $\lambda_1$ and most intense when the wavelength is $\lambda_2$. Then, the possible values of $\lambda_1$ and $\lambda_2$ areView Solution
- 5When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously, $4$ beats per second are heard. Now, some tape is attached on the prong of the fork $2$. When the tuning forks are sounded again, $6$ beats per second are heard. If the frequency of fork $1$ is $200\, Hz$, then what was the original frequency of fork $2$? .... $Hz$View Solution
- 6A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$, is emitting a sound of frequency $f_5$. The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination(s) of $u$ and $f_5$, will the sound reaching the pipe lead to a resonance?View Solution
$(A)$ $u=0.8 v$ and $f_5=f_0$
$(B)$ $u=0.8 v$ and $f_5=2 f_0$
$(C)$ $u=0.8 v$ and $f_5=0.5 f_0$
$(D)$ $u=0.5 v$ and $f_5=1.5 f_0$
- 7A string on a musical instrument is $50 cm$ long and its fundamental frequency is $270 Hz$. If the desired frequency of $1000 Hz$ is to be produced, the required length of the string is .... $cm$View Solution
- 8The power of a sound from the speaker of a radio is $20 mW$. By turning the knob of the volume control, the power of the sound is increased to $400 mW.$ The power increase in decibels as compared to the original power is .... $dB$View Solution
- 9View SolutionIt is possible to distinguish between the transverse and longitudinal waves by studying the property of
- 10A wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x)\} $ where $x$ is in metres and $t$ in seconds. The velocity of the wave is ..... $m/s$View Solution