Column $I$ shows four systems, each of the same length $L$, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $\lambda_{ f }$. Match each system with statements given in Column $II$ describing the nature and wavelength of the standing waves.
IIT 2011, Diffcult
Download our app for free and get started
In case of pipe we can produce longitudinal waves and for strings we produce transverse waves.
$A \rightarrow(p, t):$ It is a closed organ pipe hence in case of fundamental vibrations length of the tube must be $\left(\frac{1}{4}\right)^{\text {th }}$ of the wavelength (half loop).
$\frac{\lambda_t}{4}=L \Rightarrow \lambda_t=4 L$
$B \rightarrow(p, s)$ : It is open organ pipe hence in case of fundamental vibrations length of the pipe must be half of the wavelength (one loop).
$\frac{\lambda_t}{2}=L \Rightarrow \lambda_t=2 L$
$C \rightarrow(q, s)$ : It is a case of string of length $L$ fixed at both ends.
In case of fundamental vibrations length of the pipe must be half of the wavelength (one loop).
$\frac{\lambda_t}{2}=L \Rightarrow \lambda_t=2 L$
$D \rightarrow(q, r):$ In this case mid-point is fixed hence half-length must form one loop.
$\frac{\lambda_t}{2}=\frac{L}{2} \Rightarrow \lambda_t=L$
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
- 1A stationary source emits sound waves of frequency $500\, Hz$. Two observers moving along a line passing through the source detect sound to be of frequencies $480\, Hz$ and $530\, Hz$. Their respective speeds are, in $m\,s^{-1}$ (Given speed of sound $= 300\, m/s$)View Solution
- 2Consider the three wavesView Solution
${z_1},{z_2}$ and ${z_3}$ as${z_1} = A\sin (kx - \omega \,t)$, ${z_2} = A\sin (kx + \omega \,t)$ and ${z_3} = A\sin (ky - \omega \,t)$.
Which of the following represents a standing wave
- 3A sonometer wire oflength $1.5\ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 $ $kg/m^3$ and $2.2 \times 10^{11}$ $N/m^2$ respectively?View Solution
- 4In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}$$^{th}$ of the original length and the tension is changed. The factor by which the tension is to be changed, isView Solution
- 5If wavelength of a wave is $\lambda = 6000Å.$ Then wave number will beView Solution
- 6The equation of a wave is given as $y = 0.07\sin (12\pi x - 3000\pi t)$. Where $x$ is in metre and $t$ in sec, then the correct statement isView Solution
- 7Two tuning forks $A$ and $B$ produce $8\ beats/s$ when sounded together. A gas column $37.5\ cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5\ cm$ of the same gas in a similar pipe is required for a similar resonance with fork $B$. The frequencies of these two tuning forks, areView Solution
- 8The frequency of a tunning fork is $384$ per second and velocity of sound in air is $352 m/s$. How far the sound has traversed while fork completes $36$ vibration .... $m$View Solution
- 9An earthquake generates both transverse $(S)$ and longitudinal $(P)$ sound waves in the earth. The speed of $S$ waves is about $4.5\,km/s$ and that of $P$ waves is about $8.0\, km/s$. A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \,min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance about ..... $km$View Solution
- 10Following statements are given for a stationary waveView Solution
$(a)$ Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
$(b)$ All the particles cross their mean position at the same time.
$(c)$ All the particles are oscillating with same amplitude.
$(d)$ There is no net transfer of energy across any plane.
$(e)$ There are some particles which are always at rest.
Which of the following is correct