In each of the four situations of column - I, a stretched string or an organ pipe is given along with the required data. In case of strings the tension in string is T = 102.4 N and the mass per unit length of string is 1 g/m. Speed of sound in air is 320 m/s. Neglect end corrections. The frequencies of resonance are given in column - II. Match each situation in column - I with the possible resonance frequencies given in Column - II.

P - 1 ; Q - 3 ; R - 2 ; S - 4

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P - 1 ; Q - 4 ; R - 3 ; S - 2

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P - 3 ; Q - 2 ; R - 4 ; S - 1

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P - 2 ; Q - 4 ; R - 1 ; S - 3

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Solution

The correct option is B P - 1 ; Q - 4 ; R - 3 ; S - 2
(P) The fundamental frequency in the string fixed from both ends,
$f_{0} = \frac{\sqrt{\frac{T}{μ}}}{2 ℓ} = \sqrt{\frac{102.4}{1 \times 10^{- 3}}} \times \frac{1}{2 \times 0.5} H z = 320 H z .$
So, possible resonance frequencies are $f_{P} = 320 H z, 640 H z, 960 H z . . .$

(Q) The fundamental frequency in the string free from one end,
$f_{0} = \frac{\sqrt{\frac{T}{μ}}}{4 ℓ} = \frac{320}{4 \times 0.5} = 160 H z$
So, possible resonance frequencies are
$f_{Q} = 160 H z, 480 H z, 800 H z . . .$

(R) The fundamental frequency in organ pipe open at both ends is,
$f_{0} = \frac{v}{2 ℓ} = \frac{320}{2 \times 0.5} = 320 H z$
So, possible resonance frequencies are
$f_{R} = 320 H z, 640 H z, 960 H z . . .$

(S) The fundamental frequency in one end open organ pipe is
$f_{0} = \frac{v}{4 ℓ} = \frac{320}{4 \times 0.5} = 160 H z$
So, possible resonance frequencies are
$f_{S} = 160 H z, 480 H z, 800 H z . . .$

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Similar questions

Q. In each of the four situations of Column-I a stretched string or an organ pipe is given along with required data. In case of strings the tension in string is 102.4 N and the mass per unit length of string is 1 g/m. Speed of sound in air is 320 m/s. Neglect and corrections. The frequencies of resonance are given in column II. Match each situation in column-I with the possible resonance frequencies given in column-II.
Column-I Column-II
A) String fixed at both end P) 320 Hz
B) String fixed at one end and free at other end Q) 480 Hz
C) Open organ pipe R) 640 Hz
D) Closed organ pipe S) 800 Hz

Q. In each of the four situations of column-I a stretched string or an organ pipe is given along with the required data. In case of strings the tension in string is T = 102.4 N and the mass per unit length of string is 1 g/m. Speed of sound in air is 320 m/s. The length of the strings and pipes are 0.5 m. Neglect end corrections. The frequencies of resonance are given in column-II. Match each situation in column-I with the possible resonance frequencies given in Column-II

Each situation in column I gives graph of a particle moving in circular path. The variables and t represent angular speed (at any time t ), angular displacement (in time t) and time respectively. Column II gives certain resulting interpretation. Match the graphs in column I with statements in column II.

A musical instrument is made using four different metal strings. $1, 2, 3$ and 4 with mass per unit length $μ, 2 μ, 3 μ$ and $4 μ$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L_{0} and 2 L_{0} . It is found that in string- 1 (μ)$ at free length $L_{0}$ and tension $T_{0}$ the fundamental mode frequency is $f_{0} .$ List-I gives the above four strings while List-II lists the magnitude of some quantity.

	List-I		List-II
(i)	String-1 $(μ)$	(P)	$1$
(ii)	String-2 $(2 μ)$	(Q)	$1 / 2$
(iii)	String- 3 $(3 μ)$	(R)	$1 / \sqrt{2}$
(iv)	String-4 $(4 μ)$	(S)	$1 / \sqrt{3}$
		(T)	$3 / 16$
		(U)	$1 / 16$

If the tension in each string is $T_{0}$ , the correct match for the highest fundamental frequency in $f_{0}$ units will be,

The system shown below is initially in equilibrium. Masses of the blocks A, B, C, D and E are respectively 3m, 3m, 2m, 2m and 2m, Match the conditions in column-I with the effect in

Column-II.

COLUMN 1

(p) After spring 2 is cut, tension in string AB

(q) After spring2 is cut, tension in string CD

(r) After string between C and pulley is cut, tension in string AB

(s) After string between C and pulley is cut, tension in string CD

COLUMN 2

(a) increases

(b) decreases

(d) Zero

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