IIT JEE and NEET Physics @ Venkats Academy

The phenomenon in which to sound notes of slightly different frequency travelling together in the same direction are superimposed and produce alternate waxing and waning s called beats.

When the two waves are met in the same phase, they produces a maximum resultant intensity and it is called waxing. When the two waves are met in the opposite phase, they producers minimum resultant intensity and it is called waning.

We have derived a mathematical equation for beat frequency here.It is number of beats per one second.The time taken for completion of one beat that is one waxing and one waning is called time period of beat.A mathematical equation is derived for both of them as shown below.

The time interval between two maximum intensities as well as the two minimum intensities is always fixed. This is called Beat time period. The reciprocal of this time period is called beat frequency. We can derive the equation for them as shown below.

The diagrammatic view of the phenomena is as shown below.We can see one two waves are met in same phase,their resultant intensity is maximum and it is called waxing.As the time progresses,the phase difference increases and minimum intensity is produced and it is called waning.

The interval between two waxings and wanings is regular and systamatic.

Every ordinary human being needs a time interval of 0.1 second between the two successes sounds to understand the sound properly. This is called persistence of hearing. Hence difference between the frequencies of two sources shall not be greater than 10 to hear the beats.

Problem and solution

A tuning fork A has a frequency 5% more than the standard fork K and another tuning fork B has a frequency 3% less than the standard fork K. When this two tuning forks are vibrated together calculate the number of the beats generated?

Number of the beats generated is equal to difference between the frequencies.We can solve the problem as shown below.

Problem and solution

Solving problems in the concepts of beat is very simple.Just follow the concept given and comment if any clarification is required.

Heat and Thermodynamics

Thermal Convection and Radiation

Newton’s law of cooling

Wave Motion an introduction

Progressive Wave Representation and Problems

Frequency of Stationary wave in a strecthed String

Stretched String Problems and Solutions

Vibrations of Sound in Closed Pipe and Open Pipe

Vibrations of the transverse waves in a closed pipe

A pipe that is open at one end and closed at other end is called as a closed pipe.

When a sound wave is passed, at the closed end it reflects back. There is a formation of node at the close the end and anti node at the open end. Different modes of vibration are possible and in each mode of the vibration different frequency is generated. These frequencies are called harmonics and they are in a systematic way. We can derive the equation for the ratios of the frequencies as shown below.

In a closed pipe, the first and second harmonics are having the ratios of frequencies 1:3. Basing on this concept we can derive the equation for the velocity of the sound using this to vibrations as shown below. We need to calculate the vibrating lengths at which a booming sound is heard. At that particular length of the air, the frequency of the tuning fork and the frequency of the air column are coinciding with each other. They are said to be in resonance and it together produces a large booming sound.

Different modes of vibration in open pipe

The pipe that is open at both the ends is called as open pipe. When it is exposed to a sound wave at both the ends there is a formation of anti node. Under different modes of vibration different frequencies are available and the ratio is derived as shown below.

Problem and solution

A pipe that is open at both the ends as a fundamental frequency n. When one by fourth of its length is immersed in water, what will be the fundamental frequency?

When the pipe is immersed in water it becomes a closed pipe. It will further have only three by fourth of the length is one by fourth is immersed in water.