Beats- Definition, Occurrence, Beat Frequency, and Variation

Have you seen piano tuners use a technique to tune piano wires finely; they pluck the wire and a tuning fork at the same time, and then depending on the resultant sound, they will tighten or loosen the wire tension to increase or reduce the frequency thereby tuning the wire to the same frequency as the fork? This resultant sound is Beat. The beats vanish when the wire is perfectly in tune.

What is Beat?

When two waves of nearly frequency are heard at the same time, then you will notice that distinct waxing and waning of sound, this phenomenon of sound is called Beat.

Understanding of Beat

Suppose a speaker is producing sound wave and you are standing at a distance hearing the sound of some frequency (see fig.)

Now another sound source is placed nearby and produces the sound of the same frequency.

Let consider two case-

Case-1: If both the source is in the same phase, then the intensity of sound produced will be the result of two and you will listen a louder voice.

Case-2: If both the source is in the opposite phase, then the intensity will be zero and you will not listen any sound.

In the above discussion, the frequency of the second sound wave was the same. Now let's consider the frequency of the second sound wave is one less than the first frequency.Then, the interference of the two waves will be as shown in figure.where the two frequencies are in phase the sound will be louder and where out of phase,the sound will be minimum or zero. And the frequency of this occurrence will depend on the frequency of the individual sound wave.

Frequency of Beat

Frequency of Beat is the number of loudness or lowness of sound in unit time. As discussed above, the frequency of second sound was one less than the first, and we have listen loudness one time similarly if the frequency will be less by two than the first the frequency of beat will be two.

Hence, we can say that frequency of beat is equal to the difference between the two frequencies of sound.

If the frequency of first sound is F1 and frequency of second sound is F2  then,

Beat frequency

Practice Problems of Beat

Question 1:A sound of frequency 256 Hz is interfering with the sound of frequency 250 Hz frequency of beats produced will be?

Question 2: A tuning fork has the frequency 300 Hz. It is tuned with another tuning fork and producing 5 beat per second. What is the possible frequency of second tuning fork?

Answer: Frequency of second fork .

Question 3: Tuning fork A producing 8 beats per second with a fork B of frequency 340 HZ. Now prongs of A are filed a little, the bead per second decreases to 4 beats per second. Find  the frequency of A before filing.

Before filing, the beat produced is 8 bps

So, the frequency of fork A

After filing, the beat produced is 4 bps

So, the frequency of fork A

As you know, on filing the frequency of any fork increases, so after filing the frequency of fork will be higher. In this case frequency of fork before filing will be 332 Hz so that it can be 336 Hz after filing.

Hence final answer is 332 Hz.

Question 4:Two tuning forks A and B producing 5 bps together. Frequency of A is 256 Hz. now prongs of B is loaded with a little wax, the number of beats is found to increase. Calculate the frequency of B.

Answer: Frequency of tuning fork .

Then, frequency of tuning fork .

If the B is loaded with a little wax. The number of beats is found to be increased, so the difference of frequency should increase. If be consider 261 Hz,on decreasing this difference of frequency will decrease and beat frequency will also decrease.Hence correct answer is 251 Hz.

FAQs of Beat

Question 1. What is Beat?

Answer: When two sources of sound of nearly frequency difference interfere then the sound produced is known as Beat.

Question 2. What is the frequency of Beat?

Answer: Difference of two frequencies of sound is known as frequency of beat.

Question 3. Why should the frequency of two sounds be nearly equal for beat phenomena?

Answer: If frequency of sound is not nearly equal then frequency of beat will be greater and human ear can not hear this.

Question 4.  What are the uses of Beat?

Answer: Beat can be used in following ways-

1. Beats are used in determining the unknown frequencies of instruments.
2. Beats are used in determining the existence of poisonous gasses in mines.

NCERT Class 11 Physics Chapters

 Physical World Units and Measurements Motion in a Straight Line Motion in a Plane Laws of Motion Work Energy and Power Particles and Rotational Motion Gravitation Mechanical Properties of Solids Mechanical Properties in Liquids Thermal Properties of Matter Thermodynamics Kinetic Theory Oscillations Waves