Beats

Two tuning forks $A$ and $B$ sounded together give $8$ beats per second. With an air resonance tube closed at one end, the two forks give resonances when the two air columns are $32 \mathrm{cm}$ and $33 \mathrm{cm}$, respectively. Calculate the frequencies of forks.

A tuning fork of frequency $256 \mathrm{Hz}$ produces $4$ beats per second with a wire of length $25 \mathrm{cm}$ vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire be shortened so that it produces no beats with the tuning fork?

A piano wire $A$ vibrates at a fundamental frequency of $600 \mathrm{Hz}$. A second identical wire $\mathit{B}$ produces $6$ beats per second with it when the tension in $A$ is slightly increased. Find the ratio of the tension in $A$ to the tension in $B$.

A stationary observer receives sonic oscillations from two tuning forks one of which approaches and the other recedes with the same velocity. As this takes place, the observer hears the beats of frequency $f=2.0 \mathrm{Hz}$. Find the velocity of each tuning fork if their oscillation frequency is $f_o=680 \mathrm{Hz}$ and the velocity of sound in air is $v=340 \mathrm{m} {\mathrm{s}}^{-1}$.

A tuning fork $P$ of unknown frequency gives $7$ beats in $2$ seconds with another tuning fork $Q$. When $Q$ runs towards a wall with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$, it gives $5$ beats per second with its echo. On loading $P$ with wax, it gives $5$ beats per second with $Q.$ What is the frequency of $P$? Assume speed of sound $=332 \mathrm{m} {\mathrm{s}}^{-1}$.

A boy is walking away from a wall at a speed of $1.0 \mathrm{m} {\mathrm{s}}^{-1}$ in a direction at right angles to the wall. As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears $4.0$ beats per second. If the speed of sound is $340 \mathrm{m} {\mathrm{s}}^{-1}$, what is the frequency of the whistle?

Two identical violin strings, when in tune and stretched with the same tension have a fundamental frequency of $440.0 \mathrm{Hz}$. One of the strings is retuned by adjusting its tension. When this is done, $1.5$ beats per second are heard when both strings are plucked simultaneously. (a) What are the possible fundamental frequencies of the retuned string? (b) By what fractional amount was the string tension changed if it was (i) increased (ii) decreased?

A tuning fork of unknown frequency makes three beats per second with a standard fork of frequency $384 \mathrm{Hz}$. The beat frequency decreases when a small piece of wax is put on a prong of the first fork. What is the frequency of this fork?

A tuning fork produces $4$ beats per second with another tuning fork of frequency $256 \mathrm{Hz}$. The first one is now loaded with a little wax and the beat frequency is found to increase to $6$ per second. What was the original frequency of the first tuning fork?

In a liquid with density $900 \mathrm{kg} {\mathrm{m}}^{-3}$, longitudinal waves with frequency $250 \mathrm{Hz}$ are found to have wavelength $8.0 \mathrm{m}$. Calculate the Bulk modulus of the liquid.

Two sounding bodies are producing progressive waves given by, $y_1=2\sin \left(400\pi t\right)$ and $y_2=\sin \left(404\pi t\right)$, where, $t$ is in second, which superpose near the ears of a person. The person will hear

The wavelength of two sound waves are $49 \mathrm{cm}$ and $50 \mathrm{cm}$, respectively. If the room temperature is $30° \mathrm{C}$, then the number of beats produced by them is approximately (velocity of sound in air at $30° \mathrm{C}=332 \mathrm{m} {\mathrm{s}}^{-1}$ .)

Two identical wires are stretched by the same tension of $100 \mathrm{N}$ and each emits a note of frequency $200 \mathrm{Hz}$. If the tension in one wire is increased by $1 \mathrm{N}$, then the beat frequency is,

$A, B$ and $C$ are three tuning forks. Frequency of $A$ is $350\mathrm{Hz}$. The beats produced by $A$ and $B$ is $5 {\mathrm{s}}^{-1}$ and by$B$ and $C$ is $4 {\mathrm{s}}^{-1}$. When a wax is put on $A$, beat frequency between $A$ and $B$ is $2 \mathrm{Hz}$ and between $A$ and $C$ is $6 \mathrm{Hz}$. Then, frequencies of $B$ and $C$, respectively, are,

Two sound waves of wavelengths, ${\text{λ}}_1$ and ${\text{λ}}_2\left({\text{λ}}_2>{\text{λ}}_1\right)$ produce$n \mathrm{beats} {\mathrm{s}}^{-1}$. The speed of sound is,

Two sound waves of wavelength $1 \mathrm{m}$ and $1.01 \mathrm{m}$ in a gas produce $10$ beats in $3 \mathrm{s}$. The velocity of sound in the gas is