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.
Column $I$:
$(A)$ Pipe closed at one end
$(B)$ Pipe open at both ends
$(C)$ Stretched wire clamped at both ends
$(D)$ Stretched wire clamped at both ends and at mid-point
Column $II$:
$(p)$ Longitudinal waves
$(q)$ Transverse waves
$(r)$ $\lambda_{f} = L$
$(s)$ $\lambda_{f} = 2L$
$(t)$ $\lambda_{f} = 4L$

  • A
    $(A) \rightarrow p, t; (B) \rightarrow p, s; (C) \rightarrow q, s; (D) \rightarrow q, r$
  • B
    $(A) \rightarrow q, t; (B) \rightarrow r, s; (C) \rightarrow p, s; (D) \rightarrow q, t$
  • C
    $(A) \rightarrow p, t; (B) \rightarrow p, s; (C) \rightarrow q, s; (D) \rightarrow q, r$
  • D
    $(A) \rightarrow q, t; (B) \rightarrow r, t; (C) \rightarrow q, s; (D) \rightarrow s, t$

Explore More

Similar Questions

$A$ hollow pipe of length $0.8 \ m$ is closed at one end. At its open end,a $0.8 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the string is $50 \ N$ and the speed of sound in air is $320 \ m/s$,the mass of the string is: (in $g$)

$A$ vibrating string of length $\ell$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \,cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now, when the tension of the string is slightly increased, the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340 \,m/s$, the frequency $n$ of the tuning fork in $Hz$ is:

An air column in a tube $32 \,cm$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66 \,cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

An auditorium has a volume of $10^5 \ m^3$ and a surface area of absorption of $2 \times 10^4 \ m^2$. Its average absorption coefficient is $0.2$. The reverberation time of the auditorium in seconds is:

The persistence of sound in a room after the source of sound is turned off is called reverberation. The measure of reverberation time is the time required for sound intensity to decrease by $60 \,dB$. It is given that the intensity of sound falls off as $I = I_0 \exp(-c_1 \alpha)$,where $I_0$ is the initial intensity,$c_1$ is a dimensionless constant with value $1/4$. Here,$\alpha$ is a positive constant which depends on the speed of sound $v_s$,volume of the room $V$,reverberation time $t$,and the effective absorbing area $A_e$. The value of $A_e$ is the product of the absorbing coefficient and the area of the room. For a concert hall of volume $V = 600 \,m^3$,the value of $A_e$ (in $m^2$) required to give a reverberation time of $t = 1 \,s$ is closest to (speed of sound in air $v_s = 340 \,m/s$):

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo