Superposition of Waves Physics - Superposition of Waves

Find the distance between two successive antinodes in a stationary wave on s string vibrating with frequency \(32 Hz\). [Speed of wave \(=48 m / s\).

A \(36 cm\) long sonometer wire vibrates with frequency of \(280 Hz\) in fundamental mode, when it is under tensio of \(24.5 N\). Calculate linear density of the material of wire.

What are harmonics and overtones (Two Points)?

A sonometer wire 1 metre long weighing \(2 g\) is in resonance with a tuning fork of frequency \(300 Hz\). by \(5 \%\), the number of beats heard per second is 10 . Find the frequency of the tuning fork. Find tension in the sonometer wire.

A stretched sonometer wire is in unison with a tuning fork. When the length of the wire is increased by \(5 \%\), the number of beats heard per second is 10 . Find the frequency of the tuning fork.

The wavelength of two sound waves in air are \(\frac{81}{173} m\) and \(\frac{82}{171} m\). They produce 9 beats per second. Calculate Velocity of sound in air.

Show that all harmonics are present on a stretched string between two rigid supports.

In a set, 21 tuning forks are arranged in a series of decreasing frequencies. Each tuning fork produces 4 beats per second with the preceding fork. If the first fork is an octave of the last fork, find the frequencies of the first and tenth forks.

A sonometer wire is in unison with a tuning fork of frequency \(125 Hz\) when it is stretched by a weight. When the weight is completely immersed in water, 8 beats are heard per second. Find the specific gravity of the material of the weight.

Wavelengths of two notes in the air are \(\left(\frac{70}{153}\right) m\) and \(\left(\frac{70}{157}\right) m\). Each of these notes produces 8 beats per secon with a tuning fork of fixed frequency. Find the velocity of sound in the air and frequency of the tuning fork.

Distinguish between forced vibrations and resonance. Draw neat, labelled diagrams for the modes of vibration of a stretched string in second harmonic and third harmonic.

Draw neat labelled diagrams for modes of vibrations of an air column in a pipe when it is:
(a) open at both ends (b) closed at one end.
Hence derive an expression for fundamental frequency in each case.

Show that all harmonics are present in case of an air column.

What is meant by harmonics? Show that only odd harmonics are present as overtones in the case of an air column vibrating in a pipe closed at one end.

Explain the formation of stationary waves by analytical method. Show the formation of stationary wave diagrammatically.