Beats
The periodic variation in the intensity of sound at a point, due to the superposition of two sound waves of slightly different frequencies travelling in the same direction, is called beats. This note provides us an information on beats.
Summary
The periodic variation in the intensity of sound at a point, due to the superposition of two sound waves of slightly different frequencies travelling in the same direction, is called beats. This note provides us an information on beats.
Things to Remember
When two sound waves of slightly different frequencies but similar amplitudes are produced simultaneously, the loudness increases and decreases periodically which is called the beat.
The periodic variation in the intensity of sound at a point, due to the superposition of two sound waves of slightly different frequencies travelling in the same direction, is called beats.
The time interval in which one beat occurs is called beat period while the number of beat per second is called beat frequency.
MCQs
No MCQs found.
Subjective Questions
Q1:
Define communication
Type: Very_short Difficulty: Easy
Q2:
Explain the method of communication
Type: Long Difficulty: Easy
<li>
<h3>Methods of communication</h3>
<ol>
<li>
<h4>Verbal or oral communication</h4>
</li>
</ol>
<p>Verbal communication means conveying a message in terms of speaking. It is the effective method of communication, there are clarity ,accuracy, and certainty. The devices used are speech, telephone, dictating a message ,lecture ,instruction ,orders, counselling, etc.</p>
<p>There are normally two types of oral communication:</p>
<ol>
<li><strong>One way communication</strong></li>
<li><strong>Two-way communication</strong></li>
</ol>
<ol start="2">
<li>
<h4>Written communication</h4>
</li>
</ol>
<p>It is an official and more effective method of communication done by writing something and passed to others. There may or may not be two-way communication. It includes orders, instruction ,circular, letters ,newspaper, book etc.</p>
<p>It should be written clearly ,correctly and completely to make effective communication</p>
<ol start="3">
<li>
<h4>Nonverbal communication</h4>
</li>
</ol>
<p>This is the supplementary method of verbal communication where body language, expression, body posture, eye moments, proximity to the listener, appearance and pitch, tone ,speed and volume of voice are used to communicate.</p>
<p>Research suggests that only 5 % effect is produced by the spoken words ,45% by the tone, inflexion and other elements of voice and 50% by body language, movement ,eye contact,etc.</p>
<ol start="4">
<li>
<h4>Mass communication</h4>
</li>
</ol>
<p>When the message is transmitted to large mass or audience by using various medium is called mass communication. There is no face to face contact between sender and receiver. Eg radio, television, lecture ,exhibition ,etc .</p>
<ol start="5">
<li>
<h4>Listening</h4>
</li>
</ol>
<p>The key of listening message effectively is listening. Listening is a combination of hearing what another person says and psychological involvement with the person who is talking. listening requires a high level of concentration and energy(Windle & Warren, 2016) . It demands that we set aside our own thoughts and agendas ,put ourselves in another 's shoes and try to see the world through that person's eyes.</p>
<ol start="6">
<li>
<h4>Interviewing</h4>
</li>
</ol>
<p>The interview is a purposeful face to face interaction between interviewer and interviewee for getting knowledge, attitude and practice on a particular issue.</p>
<p>It is a piece of social interaction with one person asking questions and other giving answers.</p>
<ol start="7">
<li>
<h4>Counselling</h4>
</li>
</ol>
<p>Counselling is a two-way communication process by which the counselor explain in details about the problem and its solution and help the client to make a decision about his own choice. It is an effective and frequently used heath education method to identify the health problems with its cause and solution. The counselor must have certain qualities to do good counseling as friendly, sincere , cooperative ,judging capability, patience and good communication skills etc</p>
<ol start="8">
<li>
<h4>Teaching or health education</h4>
</li>
</ol>
<p>Health education is the procedure or ways in which series of activities are come out to communicate the ideas , information and develop necessary attitude and behaviour. Communication is the must and foundation of health education.</p>
<ol start="9">
<li>
<h4>Human caring / empathy</h4>
</li>
</ol>
<p>This is a non-verbal type of communication where psychological impression, feeling etc are gain by human touch ,by words and physical caring. Empathy means keeping oneself into other's shoes to invigilate in other feelings.</p>
<p> Other terminological classification of communication are :</p>
<p>_ Upward communication</p>
<p>_ Downward communication</p>
<p>_ One-way communication</p>
<p>_ Two-way communication</p>
<p>_ Formal communication</p>
<p>_ Informal communication</p>
<p>_ Vertical communication</p>
<p>_ Horizontal communication</p>
<p>_ Planned communication</p>
<p>_ Unplanned communication</p>
</li>
</ol>
Q3:
Explain the element of communication process
Type: Long Difficulty: Easy
<li>
<h4>Elements of communication process</h4>
<ol>
<li><strong>The sender</strong></li>
</ol>
<p>The sender initiates a message by encoding a thought. The sender initiates a message exactly what the receiver wants . For effective and purposeful communication, the sender must encode the message.</p>
<ol start="2">
<li><strong>Encoding</strong></li>
</ol>
<p>It is the formulation of a message in the communicator's mind that is, the sender not only translates his purpose into a message but also decides on the medium to communicate his planned message ie. Written ,verbal, signals, gesturing etc.</p>
<ol start="3">
<li><strong>Message</strong></li>
</ol>
<p>The message is the actual physical product from the sender's encoding. When we speak ,the speech is the message, when we write ,the writing is the message when we gesture ,the movement of our body parts and expressions of our faces are the message.</p>
<ol start="4">
<li><strong>Channel</strong></li>
</ol>
<p>The channel is a medium through which the message travels. It is selected by the sender according to the type of message ,area to be covered and level of the audience. Generally ,there are two channels as the formal and informal channel to transmit the message.</p>
<ol start="5">
<li><strong>Receiver</strong></li>
</ol>
<p>The receiver is the person or object, to whom the message is directed. But before the message can be received, the symbols in it must be translated into a form that can be understood by the receiver.</p>
<ol start="6">
<li><strong>Decoding</strong></li>
</ol>
<p>The steps or process of translating a message to be understandable by the receiver is known as decoding. The decoding process may differ in each individual.</p>
<ol start="7">
<li><strong>Feedback</strong></li>
</ol>
<p>Feedback is the way to check on how successful we have been in transferring our message as originally intended. It means the reacts or responds of the receiver to the sender.</p>
<ol start="8">
<li><strong>Noise</strong></li>
</ol>
<p>It can be termed as communication barrier more than an element of a communication process. It represents communication barrier that distorts the clarity of the message. There are not only noise created by voice but the others are perceptual problems, information overload, semantic difficulties, cultural difference, etc.</p>
<h4> </h4>
</li>
</ol>
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Beats
When two sound waves of slightly different frequencies but similar amplitudes are produced simultaneously, the loudness increases and decreases periodically. This phenomenon is called the beat. The periodic variation in the intensity of sound at a point, due to the superposition of two sound waves of slightly different frequencies travelling in the same direction, is called beats. The time interval in which one beat occurs is called beat period while the number of beat per second is called beat frequency.
Mathematical Derivation for Beat Frequency
Suppose two waves of frequencies f1 and f2 and each of amplitude ‘a’ are travelling in a medium in the same direction. The equations of the waves are
\begin{align*} y_1 = a\sin (\omega _1 t – k_1x) \dots (i) \\ y_2 = a\sin (\omega _2 t – k_2x) \dots (ii) \\ \text {where,} \: \omega _1 = 2\pi f_1 \: \text {and} \: \omega _2 = 2\pi f_2.\end{align*}
When two waves superpose
\begin{align*} \text{at x} = o, \: \text {then } \\ y_1 = a\sin \omega _1 t \dots (iii) \\ y_1 = a\sin \omega _2 t \dots (vi) \\ \end{align*}
And from the superposition principle the resultant displacement at that point is given by
\begin{align*}\\y = y_1 + y_2 \\ = a\sin \omega _1 t + a\sin \omega _2 t \\ =2a\sin \left (\frac {\omega _1 + \omega _2}{2}\right ) t \cos \left (\frac {\omega _1 - \omega _2}{2}\right )t \\ =2a\cos 2\pi \left (\frac {f_1 – f_2}{2} \right ) t \sin 2\pi \left (\frac {f_1 + f_2}{2} \right ) t \\ \text {or,} \: y = A\sin 2\pi \left (\frac {f_1 + f_2}{2} \right ) t \\ \text {where A} \: = \: 2a\cos 2\pi \left (\frac {f_1 – f_2}{2} \right ) t. \: \\\end{align*} The above equation shows that resultant wave has an amplitude A that depends on time t and varies with a frequency of f \begin{align*}= \frac {f_1 – f_2}{2}. \end{align*}
Condition for Maxima
The resultant amplitude A will be maximum when
\begin{align*} \: \cos 2\pi \left ( \frac {f_1 – f_2}{2}\right ).t \: \text {is maximum. That is,} \\ \cos 2\pi \left ( \frac {f_1 – f_2}{2}\right ).t = \pm 1 \\ \text {or,} \: \cos 2\pi \left ( \frac {f_1 – f_2}{2}\right ).t = \cos n\pi \\ \text {where n} = 0, 1, 2, 3, 4, \dots \\ \text {So,} \: 2\pi\left ( \frac {f_1 – f_2}{2}\right ).t = n\pi \\ \text {or,} \: t = \frac {n}{f_1 – f_2} \\ \text {or,} \: t = 0, \frac {1}{f_1 – f_2}, \frac {2}{f_1 – f_2}, \frac {3}{f_1 – f_2}, \dots \\ \end{align*}
The time interval between two consecutive maxima is the period and it is given by
\begin{align*} \\ T = \frac {1}{f_1 – f_2} – 0\: \text {or,} \:\frac {2}{f_1 – f_2} - \frac {3}{f_1 – f_2} \: \text {or,} \dots = \frac {1}{f_1 – f_2} \\ \therefore T = \frac {1}{f_1 - f_2} \\ \text {Hence frequency of maxima} \: = \frac 1T = f_1 – f_2 \\ \end{align*}
Condition for Minima
The resultant amplitude A will be minimum when
\begin{align*} \: \cos 2\pi \left (\frac {f_1 – f_2}{2}\right )t \: \text {is miniimum. } \\ \text {That is,} \\ \cos 2\pi \frac {f_1 – f_2}{2}.t = 0 \\ \text {or,} \: \cos 2\pi \left (\frac {f_1 – f_2}{2}\right ). t = \cos (2n + 1)\pi/2 \\ \text {where n} = 0, 1, 2, 3, 4, \dots \\ \text {So,} \: 2\pi\left ( \frac {f_1 – f_2}{2}\right ).t = (2n + 1)\pi/2 \\ \text {or,} \: t = \frac {2n + 1}{2(f_1 – f_2)} \\ \text {or,} \: t = \frac {1}{2(f_1 – f_2)}, \frac {3}{2(f_1 – f_2)}, \frac {5}{2(f_1 – f_2)}, \dots \\ \end{align*}
So, the time interval between two consecutive minima i.e. beat period is given as,
\begin{align*} \\ T = \frac {3}{2(f_1 – f_2)} - \frac {1}{2(f_1 – f_2)} \: \text {or,} \: \frac {5}{2(f_1 – f_2)} - \frac {3}{2(f_1 – f_2)} \\ = \frac {1}{f_1 – f_2} \\ \text {Hence, frequency of minima} = \frac 1T = f_1 – f_2, \text {same as the frequency of maxima. } \end{align*}.So, the beat frequency is equal to the difference of frequencies of two sound waves.
References
Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.
S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.
Lesson
Acoustic Phenomena
Subject
Physics
Grade
Grade 12
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