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Important Questions on Wave Motion on a String

HARD

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire is

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe which is $L$ meter long. The length of the open pipe will be

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

In sonometer experiment, the string of length $L$ under tension vibrates in second overtone between two bridges. The amplitude of vibration is maximum at

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencier between these two. The lowest resonant frequency for this string is:

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, $y\left(x, t\right)=0.5\sin \left(\frac{5\pi }{4}x\right)\cos \left(200\pi t\right)$. What is the speed of the travelling wave moving in the positive $x$ direction? ($x$ and $t$are in meter and second, respectively)

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

The fundamental frequency of an air column in a pipe closed at one end is $100 \mathrm{Hz}$. If the same pipe is open at both the ends, the frequencies produced in $\mathrm{Hz}$ are

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

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:

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A sonometer wire of length $1.5\mathrm{m}$ is made of steel. The tension in it produces an elastic strain of $\text{1\%}$. 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?

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

The fundamental frequency of a closed organ pipe of length $20 \mathrm{cm}$ is equal to the second overtone of an organ pipe open at both the ends. The length of the organ pipe open at both the ends is

HARD

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

EASY

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50\text{cm}$. The next larger length of the column resonating with the same tuning fork is:

HARD

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

The total length of a sonometer wire fixed between two bridges is $110 \mathrm{cm}$. Now, two more bridges are placed to divide the length of the wire in the ratio $6:3:2$. If the tension in the wire is $400 \mathrm{N}$ and the mass per unit length of the wire is $0.01 \mathrm{kg} {\mathrm{m}}^{-1}$, then the minimum common frequency with which all the three parts can vibrate, is

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

Two wires $W_1$ and $W_2$ have the same radius $r$and respective, densities ${\rho }_1$ and ${\rho }_2$, such that ${\rho }_2=4{\rho }_1$ . They are joined together at the point $O$, as shown in the figure. The combination is used as a sonometer wire and kept under tension $T$. The point $O$ is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $W_1$ to $W_2$ is 

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A granite rod of $60 \mathrm{cm}$ length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ and its Young's modulus is $9.27\times {10}^{10} \mathrm{Pa}$. What will be the fundamental frequency of the longitudinal vibrations?

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A wire of length $2\mathrm{L},$ is made by joining two wires $\mathrm{A}$ and $\mathrm{B}$ of same length but different radii $\mathrm{r}$ and $2\mathrm{r}$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $\mathrm{A}$ is $\mathrm{p}$ and that in $\mathrm{B}$ is $\mathrm{q}$ then ratio $\mathrm{p}:\mathrm{q}$ is:

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300 \mathrm{m}/\mathrm{s},$ the frequency difference between the fundamental and second harmonic of this pipe is __________ Hz.

HARD

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

The end correction of a resonance column is $1 \mathrm{cm}$. If the shortest length resonating with the tuning fork is $10 \mathrm{cm}$, the next resonating length should be

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. A tuning fork of frequency $512\mathrm{ }\mathrm{Hz}$ produces first resonance when the tube is filled with water to a mark $11\mathrm{ }\mathrm{cm}$ below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency $256\mathrm{ }\mathrm{Hz}$ which produces first resonance when water reaches a mark $27\mathrm{ }\mathrm{cm}$ below the reference mark. The velocity of sound in air, obtained in the experiment, is close to

MEDIUM

Physics>Oscillations and Waves>Wave Motion on a String>Standing Waves on a String

A closed organ pipe has a fundamental frequency of $1.5\mathrm{kHz}$. The number of overtones that can be distinctly heard by a person with this organ pipe will be $($Assume that the highest frequency a person can hear is $\mathrm{20,000}\mathrm{Hz}$).