G L Mittal and TARUN MITTAL Solutions for Chapter: Vibrations of Stretched Strings, Exercise 2: NUMERICALS

A tuning fork produces $5$ beats/second with a sonometer wire of length $40 \mathrm{cm}$. When the length of the wire is decreased by $1 \mathrm{cm}$, again the same number of beats per second are heard. Calculate the frequency of the fork.

The frequency of a brass wire is $240 \mathrm{Hz}$ when its tension is $625 \mathrm{N}$. If its tension is decreased to $100 \mathrm{N}$ and length halved, what will be its frequency?

The frequency of a sonometer wire is $100 \mathrm{Hz}$. On doubling the length of the wire and changing tension, the frequency become $75 \mathrm{Hz}$. Determine the ratio of the initial and final tensions.

The ratio of frequencies of two wires having same length and same tension and made of the same material is $2:3$. If the diameter of one wire be $0.09 \mathrm{cm}$, then determine the diameter of the other.

Two forks A and B when sounded together produce $4$ beats/second. The fork A is in unison with $30 \mathrm{cm}$ length of a sonometer wire and B is in unison with $25 \mathrm{cm}$ length of the same wire at the same tension. Calculate the frequencies of the forks.

A weight is suspended from a sonometer wire. When the length of the wire between the bridges is $80 \mathrm{cm}$, the wire is found in unison with a tuning fork. But when an additional $0.1 \mathrm{kg}$ weight is suspended from it then, to keep it in unison with the same fork, its length between the bridges is to be increased by $1 \mathrm{cm}$. What weight was suspended from the wire in the beginning?

A tuning fork is marked $256$ number. What does it indicate? It is in unison with the wire of a sonometer whose length is $81 \mathrm{cm}$ and which is under a tension of $4 \mathrm{kg}$. How can this wire be brought in unison with a fork marked $384$ by (i) changing the tension only, (ii) changing the length only?

A tuning fork is marked‌ $256$ number. What does it indicate? It is in unison with the wire of a sonometer whose length is $81 \mathrm{cm}$ and which is under a tension of $4 \mathrm{kg}$. How can this wire be brought in unison with a fork marked $384$ by (i) changing the tension only, (ii) changing the length only?