Embibe Experts Solutions for Chapter: Sound Waves, Exercise 3: Exercise - 3

A vibrating string of a certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \mathrm{cm}$ inside a tube closed at one end. The string also generates $4 \mathrm{beats} \mathrm{per} \mathrm{second}$ when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased, the number of beats reduces to $2 \mathrm{per} \mathrm{second}$. Assuming the velocity of sound in air to be $340 \mathrm{m} {\mathrm{s}}^{-1}$, the frequency $n$ of the tuning fork in $\mathrm{Hz}$ is 

A student performed the experiment to measure the speed of the sound in air using the resonance air-column method. Two resonances in the air column were obtained by lowering the water level. The resonance with the shorter air column is the first resonance and that with the longer air column is the second resonance. Then

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 {\mathrm{s}}^{-1}$. He told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $\left(0.350\pm 0.005\right) \mathrm{m}$, the gas in the tube is (useful information: $\sqrt{167RT}=640 {\mathrm{J}}^{\frac{1}{2}} \mathrm{mole}{ }^{-\frac{1}{2}}, \sqrt{140RT}=590 {\mathrm{J}}^{\frac{1}{2}} \mathrm{mole}{ }^{-\frac{1}{2}}$. The molar mass $M$ in grams and given in the options. Take the values of $\sqrt{\frac{10}{M}}$ for each gas as given there). 

A sound absorber attenuates the sound level by $20 \mathrm{dB}$. The intensity decreases by a factor of

 A motorcycle starts from rest and accelerates along a straight path at $2 \mathrm{m} {\mathrm{s}}^{-2}$. At the starting point of the motorcycle, there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motorcycle was at rest? (speed of sound = $330 \mathrm{m} {\mathrm{s}}^{-1}$)

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 $340 \mathrm{m}/\mathrm{s}$.

A train is moving on a straight track with speed $20 \mathrm{m} {\mathrm{s}}^{-1}$. It is blowing its whistle at the frequency of $1000 \mathrm{Hz}$. The percentage change in the frequency heard by a person standing near the track of the train as the train passes him is (speed of sound $=320 \mathrm{m} {\mathrm{s}}^{-1}$) close to

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now