Column I shows four systems, each of the same length , for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as . Match each system with statements given in Column

Question

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 $λ_{f}$ . Match each system with statements given in Column II describing the nature and wavelength of the standing waves. [2011]

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

Smart Achievers · Accepted Answer

(1)

(A) Pipe closed at one end

Waves produced are longitudinal

$\frac{λ_{f}}{4} = L$

$∴$ $λ_{f} = 4 L$

(B) Pipe open at both ends

waves produced are longitudinal

$\frac{λ_{f}}{2} = L$

$∴$ $λ_{f} = 2 L$

(C) Stretched wire clamped at both ends

Waves produced are transverse in nature.

$\frac{λ_{f}}{2} = L$

$∴$ $λ_{f} = 2 L$

(D) Stretched wave clamped at both ends and at mid point

Waves produced are transverse in nature

$λ_{f} = L$

Solution

1 $A - p, t; B - p, s; C - q, s; D - q, r$

2 $A - q, r; B - p, s; C - q, s; D - p, t$

3 $A - q, r; B - q, s; C - p, s; D - p, t$

4 $A - p, s; B - q, s; C - q, r; D - p, t$

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Solution

1 A-p,t; B-p,s; C-q,s; D-q,r

2 A-q,r; B-p,s; C-q,s; D-p,t

3 A-q,r; B-q,s; C-p,s; D-p,t

4 A-p,s; B-q,s; C-q,r; D-p,t

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1 $A - p, t; B - p, s; C - q, s; D - q, r$

2 $A - q, r; B - p, s; C - q, s; D - p, t$

3 $A - q, r; B - q, s; C - p, s; D - p, t$

4 $A - p, s; B - q, s; C - q, r; D - p, t$