Beats

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The melodious sound of the piano and tuning fork is enjoyed by many. The sound you hear when you strike the black and white keys on your keyboard is the result of two sound waves colliding. The alternating loudness and softness of these superimposed waves is referred to as a beat.

Table of Content

Beats: Introduction
When do Beats Happen?
Beat Frequency: Definition
Sample Questions

Beats: Introduction

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The phenomenon of 'beats' arises from the superposition of waves.

We hear a sound of similar frequency (the average of two close frequencies) when two harmonic sound waves of close (but not equal) frequencies are heard at the same moment, but we also hear something else.

At a frequency equivalent to the difference between the two close frequencies, we perceive distinctly distinct rising and fading of the sound strength. Because a wave not only travels through space but also through time, if two waves can produce interference when they overlap in space, they should also produce an interference pattern when they overlap in time, this phenomenon is known as beats.

When do Beats Happen?

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Beats happen when two waves of nearby frequencies collide and form a new wave. To understand this phenomenon, let's try an experiment.

We'll need two tuning forks with similar frequencies, such as 700 and 705 Hz. When played separately, both frequencies are nearly identical, and there is no detectable difference in the audible frequency you hear.

However, when played together, these two frequencies interfere with each other, and because they are so close in frequency, their crest-crest interference produces constructive interference, increasing the amplitude of the wave.

Beats

Beats

When a crest and trough collide, the interference produced is destructive, so they both cancel out and the amplitude produced is equal to zero, so the loudness is reduced to zero. The beat frequency is the frequency at which the loudness increases and decreases, and it is equal to the difference between the two frequencies that produced it.

Because frequency A is 700 Hz and frequency B is 705 Hz in our scenario, the resultant beat frequency will be 705-700 Hz = 5 Hz if the two frequencies collide in time.

By listening to the beats of two near frequencies, we may determine the difference between them; the closer the two frequencies are, the smaller the resultant frequency. To finely tune piano wires, piano tuners use this technique of beats and interference. They pluck the wire and a tuning fork at the same time, and then tighten or loosen the wire tension to increase or reduce the frequency, thereby tuning the wire to the same frequency as the fork. The beats eventually vanish when the wire is perfectly in tune.

Beat Frequency: Definition

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When two sound waves of different frequencies collide, their amplitudes are alternately added and subtracted over a particular time period, resulting in the beat frequency. As a result, the sound becomes increasingly louder and weaker. Beats are created when two waves of almost identical frequencies travelling in the same direction collide at a spot.

The beat frequency is equal to the total value of the frequency difference between the two waves. Beat frequency is the number of beats per second that is equal to the difference in frequencies of two waves.

Sample Questions

Ques: A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to? (2 marks)

Ans: Frequency of the sound produced by the open flute

f=2(v/2l) = (2 x 330)/(2 x 0.5) = 660 Hz

Velocity of observer, v0 = 10 x (5/18) = (25/9) m/s

According to the Doppler effect:

Frequency detected by observer

f’ = {(v + v0)/v}f = {((25/9) + 330)/330}660

= 2 ((25/9) + 330)

f’ = 665.55 ≈ 666 Hz

Ques: Two sources of sound S₁ and S₂ produce sound waves of the same frequency 660 Hz. A listener is moving from source S₁ towards S₂ with constant speed u m/s and he hears 10 beats. The velocity of sound is 330 m/s. Then u is equals? (1 mark)

Ans: f₁ = f[(v – v0)/v]

f₂ = f[(v + v0)/v]

Frequency f₂ – f₁= f x (2v0/v)

10 = 660 x (2u/330)

u = 2.5 m/s

Ques: Three sound waves of equal amplitudes have frequencies(f-1, f, f+1). They superimpose to give beats. The number of beats produced per unit time will be? (2 marks)

Ans: Beat produced between(f-1) and f is 1.

Beat produced between f and f+1 is 1.

Beat produced between(f-1) and (f+1) is 2

So, No of beats produced per second will be 2

Ques: A source of sound S moving with a velocity of 50 m/s towards the observer who is stationary. The observer measures the frequency of the source when it is moving away from the observer after the source has crossed the observer? (Take the velocity of sound in air as 350 m/s) (2 marks)

Ans: When source is moving towards a stationary observer,

f_app = f_source {(V – 0)/(V – 50)}

1000 = f_source (350/300)

When source is moving away from observer

f’ = f_source{350/(350 + 50)}

f’ = {(1000 x 300)/350} x (350/400)

f’ = 750 Hz

Ques: Write Beats' real-world applications. (2 marks)

Ans: The following are some examples of how we employ beats:

For the purpose of tuning musical instruments.
In the development of low-frequency oscillators.
To determine the presence of hazardous gases in mines.

CBSE CLASS XII Related Questions

1.
Read the following paragraph and answer the questions that follow.
A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.

2.
A charged particle $+q$ in an electric field $\vec{E}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{B}$. But this magnetic force is perpendicular to both velocity $\vec{v}$ of the charged particle and the magnetic field $\vec{B}$, so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses $m$ and $\frac{m}{2}$ having charges $-q$ and $+2q$ respectively. They are accelerated from rest through the same potential difference $V$ and acquire kinetic energy $K_1$ and $K_2$. Then they enter in a region of uniform magnetic field $\vec{B}$ perpendicular to their velocities.

3.
The resistance of a metal wire at $ 20^\circ \text{C} $ is $ 1.05 \, \Omega $ and at $ 100^\circ \text{C} $ is $ 1.38 \, \Omega $. Determine the temperature coefficient of resistivity of this metal.

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4.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

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5.
Read the following paragraph and answer the questions that follow.
In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.

6.
Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance $U = \frac{1}{2}CV^2$, where symbols have their usual meanings.
Two capacitors, one of $3 \ \mu$F and the other of $6 \ \mu$F, are connected in series in the circuit as shown in the figure, for a long time. }

Beats

Beats: Introduction

When do Beats Happen?

Beat Frequency: Definition

Sample Questions

CBSE CLASS XII Related Questions

3.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

4.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

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Beats

Beats: Introduction

When do Beats Happen?

Beat Frequency: Definition

Sample Questions

CBSE CLASS XII Related Questions

3. The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

4.Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

Comments

SUBSCRIBE TO OUR NEWS LETTER

3.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

4.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.