Standing Waves

In a sonometer wire the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has volume of 0.0075m^​3. The fundamental frequency of the wire is 260Hz. Find the new fundamental frequency if the suspended mass is completely submerged in water

The fundamental frequencies of two copper wire of same length are in the ratio $1:2$. If the tension on the wires are$729 \mathrm{g}$ and $324 \mathrm{g}$ respectively, then the ratio of their diameters will be:

A string of length $1 \mathrm{m}$ and mass $2\times {10}^{-5} \mathrm{kg}$ is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies $750 \mathrm{Hz}$ and $1000 \mathrm{Hz}$. The value of tension $T$ is _____ newton.

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:

A wire of density $8\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$ is stretched between two clamps $0.5 \mathrm{m}$ apart. The extension developed in the wire is $3.2\times {10}^{-4} \mathrm{m}$. If $Y=8\times {10}^{10} \mathrm{N} {\mathrm{m}}^{-2}$, the fundamental frequency of vibration in the wire will be _____ $\mathrm{Hz}$

A guitar string of length $90 \mathrm{cm}$ vibrates with a fundamental frequency of $120 \mathrm{Hz}$. The length of the string producing a fundamental of $180 \mathrm{Hz}$ will be _____ $\mathrm{cm}$

In an experiment with sonometer when a mass of $180 \mathrm{g}$ is attached to the string, it vibrates with fundamental frequency of $30 \mathrm{Hz}$. When a mass $m$ is attached, the string vibrates with fundamental frequency of $50 \mathrm{Hz}$. The value of $m$ is ______ $\mathrm{g}$.

For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is $405 \mathrm{Hz}$ and the speed of sound in air is $324 \mathrm{m} {\mathrm{s}}^{–1}$ the length of the organ pipe is _____ $\mathrm{m}$.

The fundamental frequency of vibration of a string between two rigid support is $50 \mathrm{Hz}$. The mass of the string is $18 \mathrm{g}$ and its linear mass density is $20 \mathrm{g} {\mathrm{m}}^{-1}$. The speed of the transverse waves so produced in the string is _______ $\mathrm{m} {\mathrm{s}}^{–1}$.

An organ pipe $40 \mathrm{cm}$ long is open at both ends. The speed of sound in air is $360 \mathrm{m} {\mathrm{s}}^{-1}$. The frequency of the second harmonic is _$\_\_\_\_\_\_\_\_ \mathrm{Hz}.$

A standing wave $y=A\sin \left(\frac{20\pi x}{3}\right) \cos \left(1000\pi x\right)$is maintained in a taut string where $y$ and $x$ are expressed in meters. The distance between the successive points oscillating with the amplitude$\frac{A}{2}$ across a node is equal to

A $100 \mathrm{cm}$ string fixed at both ends produces successive resonance frequency $384 \mathrm{Hz}$ and $288 \mathrm{Hz}$. Wave speed in string is $24n$ $\mathrm{m} {\mathrm{s}}^{-1}$. Find the value of$n$.

When a tuning fork vibrates with $1.0 \mathrm{m}$ or $1.05 \mathrm{m}$ long wire (both in same mode), $5$ beats per second are produced in each case. If the frequency of the tuning fork is $5f$ (in $Hz$) find$f$.

 An open organ pipe of length $L$ vibrates in second harmonic mode. The pressure vibration is maximum 

A $100 \mathrm{cm}$ string fixed at both ends produces successive resonance frequency $384 \mathrm{Hz}$ and $288 \mathrm{Hz}$. Wave speed in string is $16P \mathrm{m} {\mathrm{s}}^{-1}$, then$P$ is

Equation of a stationary wave can be expressed as $y=8\sin \frac{\pi x}{4} \cos 20\pi t$ here$x$and $y$ are in cm and$t$ in second, wavelength of any component of  progressive wave is

Write down an expression for the fundamental frequency of transverse vibration of a stretched string. If the vibrating wire is touched lightly at a point $\frac{1}{3}$rd distance from one end, what will happen?

A string vibrates with a frequency of $210 \mathrm{Hz}$. Another frequency with which the string can vibrate is $300 \mathrm{Hz}$. The number of harmonic of the first frequency is

The INCORRECT statement is

Discuss the formation of standing waves in a closed pipe. Show the sixth harmonic of vibration in the closed pipe with a diagram. How many nodes and antinodes are present?