Maharashtra Board Solutions for Chapter: Superposition of Waves, Exercise 4: Exercises

A standing wave is produced in a tube open at both ends. The fundamental frequency is $300 \mathrm{Hz}$. What is the length of tube? (speed of  the sound $= 340 \mathrm{m} {\mathrm{s}}^{-1}$).

Find the fundamental, first overtone and second overtone frequencies of a pipe, open at both the ends, of length $25 \mathrm{cm}$ if the speed of sound in air is $330 \mathrm{m}/\mathrm{s}$.

A pipe open at both the ends has a fundamental frequency of $600 \mathrm{Hz}$. The first overtone of a pipe closed at one end has the same frequency as the first overtone of the open pipe. How long are the two pipes? (Take the velocity of sound to be $330 \mathrm{m}/\mathrm{s}$).

A string $1 \mathrm{m}$ long is fixed at one end. Transverse vibrations of frequency $15 \mathrm{Hz}$ are imposed at the free end. Due to this, a stationary wave with four complete loops, is produced on the string. Find the speed of the progressive wave which produces the stationary wave.

A violin string vibrates with fundamental frequency of $440 \mathrm{Hz}$. What are the frequencies of first and second overtones?

A set of $8$tuning forks is arranged in a series of increasing orders of frequencies. Each fork gives $4$ beats per second with the next one and the frequency of the last fork is twice that of the first. Calculate the frequencies of the first and the last fork. 
 

A sonometer wire is stretched by tension of $40 \mathrm{N}$. It vibrates in unison with a tuning fork of frequency 3$84 \mathrm{Hz}$. How many numbers of beats get produced in two seconds if the tension in the wire is decreased by $1.24 \mathrm{N}$?

The string of a guitar is $80 \mathrm{cm}$ long and has a fundamental frequency of $112 \mathrm{Hz}$. If a guitarist wishes to produce a frequency of $160 \mathrm{Hz}$, where should the person press the string?