If {n₁},{n₂},{n₃}......... are frequencies of segments of a stretched string, frequency n of s

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14.Waves and Sound

medium

If ${n_1},{n_2},{n_3}.........$ are the frequencies of segments of a stretched string, the frequency $n$ of the string is given by

$n = {n_1} + {n_2} + {n_3} + .......$

$n = \sqrt {{n_1} \times {n_2} \times {n_3} \times .......} $

$\frac{1}{n} = \frac{1}{{{n_1}}} + \frac{1}{{{n_2}}} + \frac{1}{{{n_3}}} + .....$

None of these

Solution

${n_1}{l_1} = {n_2}{l_2} = {n_3}{l_3}….. = $constant $= k$ (say) $= nl$

Also ${l_1} + {l_2} + {l_3} + {l_4} + …… = 1$

$\frac{k}{{{n_1}}} + \frac{k}{{{n_2}}} + \frac{k}{{{n_3}}} + \frac{k}{{{n_4}}} + …. = \frac{k}{n}$==> $\frac{1}{n} = \frac{1}{{{n_1}}} + \frac{1}{{{n_2}}} + \frac{1}{{{n_3}}} + …….$

Standard 11

Physics

A stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1(figure)$. At an instant this particle is at mean positions and is moving towards its negative extreme. Which of the following set of particles, are in same phase with particle $1$

easy

A hollow pipe of length $0.8 \mathrm{~m}$ is closed at one end. At its open end a $0.5 \mathrm{~m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \mathrm{~N}$ and the speed of sound is $320 \mathrm{~ms}^{-1}$, the mass of the string is

normal

(IIT-2010)

Standing waves are produced in $10 \,m$ long stretched string fixed at both ends. If the string vibrates in $5$ segments and wave velocity is $20 \,m / s$, the frequency is ……. $Hz$

easy

If $n _{1}, n_{2}$ and $n _{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

medium

(AIPMT-2014)

The length of a son meter wire $AB$ is $110\; cm$. Where should the two bridges be placed from $A$ to divide the wire in $3$ segments whose fundamental frequencies are in the ratio of $1:2:3$?

medium

(AIPMT-1995)

If ${n_1},{n_2},{n_3}.........$ are the frequencies of segments of a stretched string, the frequency $n$ of the string is given by

Solution

Similar Questions

A stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1(figure)$. At an instant this particle is at mean positions and is moving towards its negative extreme. Which of the following set of particles, are in same phase with particle $1$

Standing waves are produced in $10 \,m$ long stretched string fixed at both ends. If the string vibrates in $5$ segments and wave velocity is $20 \,m / s$, the frequency is ……. $Hz$

If $n _{1}, n_{2}$ and $n _{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

The length of a son meter wire $AB$ is $110\; cm$. Where should the two bridges be placed from $A$ to divide the wire in $3$ segments whose fundamental frequencies are in the ratio of $1:2:3$?

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