Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Stationary Waves, Exercise 3: Competitive Thinking

A wire of density $9\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ is stretched between two clamps $1 \mathrm{m}$ apart and is subjected to an extension of $4.9\times {10}^{-4} \mathrm{m}.$ What will be the lowest frequency of transverse vibration in the wire ? (Young's modulus of material $=9\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}.$)

A tuning fork of frequency $340 \mathrm{Hz}$ is vibrated just above the tube of $120 \mathrm{cm}$ height. Water is poured slowly into the tube. What is the minimum height of water necessary for the resonance? (speed of sound in the air$=340 \mathrm{m} {\mathrm{s}}^{-1}$)

An organ pipe closed at one end has fundamental frequency of $1500$ $\mathrm{Hz}$. The maximum number of overtones generated by this pipe which a normal person can hear is,

What is phase difference between two waves if the resultant amplitude due to their superposition is same as that of the waves? 

In Melde's experiment, in parallel position when mass $m_1$ is kept in the pan, then the number of loops obtained is $p_1$ and when mass $m_2$ is kept the number of loops is $p_2$; then the mass of pan $m_0$is

A pipe of:length $85 \mathrm{cm}$is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250 \mathrm{Hz}$. The velocity of sound in air is $340 \mathrm{m} {\mathrm{s}}^{-1}$.

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made $\frac{1}{3}$ and closed pipe is made three times the original, the number of beats produced will be 

A sonometer wire of length $1.5 \mathrm{m}$ is made of steel. The tension in it produces an elastic strain of $1 \% .$ What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times {10}^3\mathrm{kg} {\mathrm{m}}^{-3}$ and $2.2\times {10}^{11}\mathrm{N} {\mathrm{m}}^{-2}$ respectively?