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The different cases of the Doppler’s effect is discussed as follows:-

When the source of the sound is moving towards the observer and the observer is moving towards the source of sound.

Consider source of the sound ‘s’ moving towards the observer with velocity and observer is moving towards the source of sound with velocity vo. If source of sound and observer is at rest and if v be the velocity of sound, then the frequency of sound heard by observer = v/l where be the wavelength of sound emitted by source of sound.

Since, source of sound is moving towards the observer.

Then,

Where f is the frequency of sound emitted by source of sound.

Again, the observer is in motion

This is the changed frequency, when resource of sound is moving towards the observer and observer is moving towards the source of sound. When the observer is moving towards the stationary source of sound. When the observer is moving towards the stationary source of sound with velocity v_{o}. And be the frequency of sound emitted by source of the sound and if the source of the sound and observer is at rest. Then the frequency of sound heard by observer.

Here,

The source of sound is at rest and observer is in motion since the source of sound is rest then the wavelength of sound,

But observer is in motion, the relative velocity of sound with respect to the observer

This is the apparent frequency when the observer is moving towards the stationary source of s.

Relation between intensity and amplitude of wave.

Suppose the displacement y of the vibration layer of air is given by,

Y=asinωt

Where, A is the amplitude of wave and w is the angular velocity (frequency) of wave

The velocity of vibration layer of air is given by.

And hence corresponding k e is given by,

Where m is the mass of layer. The layer also has potential energy. And from SHM the total energy of particle executing SHM is maximum KE

i.e. the total energy of vibration air of layer is given by,

^{ }In 1sec. air is disturbed by the wave to a distance of v meter where v is the velocity of the sound. If the cross sectional area of the air is taken as then the volume of air disturbed by sound is vm^{3}

M = Sμ

Where S is the density of air.

Then,

This is the energy crossing a unit area per second then by depth of intensity of the sound E is I.

i. e. the intensity of the sound of a given frequency is directly proportional to the square of amplitude.

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]]>The post Beat appeared first on Reference Notes.

]]>The no of hearing produce in one second is beat frequency.

Consider two waves having frequency f_{1} and f_{2} then the displacement equation of these two waves are given by.

If the two waves are sounded together, they will interfere and the resulting displacement y according to the principle of super position is given by,

Since, intensity of sound is related to the amplitude of sound.

The intensity will be maximum.

i.e. the intensity of sound will be minimum in the time

The consecutive time internal between the hearing two minimum intensity of sound

Since the consecutive time internal between maximum or minimum intensity of sound is called beat period.

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]]>The post Intensity of sound appeared first on Reference Notes.

]]>The intensity of sound at a point is defined as the amount of sound energy crossing the point per unit area per second. Then the unit of intensity of the sound is given by j/m^{2}s or wm^{-2}.

The threshold of hearing is the lowest intensity of the sound that can be detected by our ear within the range of audibility. The sensitivity of ears caries with the frequency i.e. the sensitivity of ears is different range of frequencies. Also the threshold of hearing at a frequency may very form ear to ear. Hence, the threshold of hearing has been defined for a normal ear at a frequency of 1000 Hz. The threshold of hearing is taken as 10^{-12} watt m^{-2} for frequency of 1000Hz.

** **

Since, we know,

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]]>The post Characteristics of musical sound appeared first on Reference Notes.

]]>The pitch is the characteristics of a musical sound which depends upon the frequency. The sound with low frequency is low pitch able sound and the sound with high frequency is high pitch able sound.

The loudness of musical sound is related to the intensity of the sound the higher is the intensity, the higher will be the loudness. If Ibe the intensity of the sound, then the loudness is related to the I as,

It measure the complexity of sound. Quality of sound depends upon the number and intensity of harmonics. Present in the sound. A pure sound produces comparatively less pleasing effect on ears then sound consisting of a no of harmonics. Usually a sounding body produce a complex sound of frequency. The f_{0}, 2f_{0}, 3f_{0}, etc. where to is called fundamental frequency. The f_{0}, 2f_{0}, 3f_{0}…………etc are called first, 2^{nd}, 3^{rd} ………… harmonics. In the voice of different peoples different harmonics are present. Due to the different harmonics present in the voices, we characteristics of sound is called Quality or Timber.

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]]>The post Vibration in the stretched string appeared first on Reference Notes.

]]>When a string of mass per unit length (m) under the action of tension; T; is set in to transverse vibration the velocity of the wave propagation through the string is given by

m = t\m

In such a vibration of the string the disturbance produced at one fixed end. Travels along the string and gets reflected back at the other end, since the original wave and reflect wave have the same frequency and amplitude, they superimpose to produce stationary transverse wave.

In this mode of vibration, the string vibration in one segment. This there are two nods at fixed ends and an antinode in between them. If ‘λ’ be the length of string and λ_{0} be the wave length of wave in this mode of vibration.

If ‘U’ be the velocity of wave and to be the frequency of wave in this mode of vibration

This is the fundamental frequency or frequency of 1^{st} harmonics.

** **In this mode of vibration the string vibration in two segments. Thus there are three nodes and two antinodes between of string and l_{1} be the wavelength of wave in this mode of vibration.

l = λ_{1}

If u be the velocity of wave and f_{1} be the frequency of wave in this mode of vibration.

This is the frequency of 1^{st} overtone and 2^{nd} harmonics.

** **

** ** 4 nodes & 3 AN

This is the frequency of 2^{nd} overtone or 3^{rd} harmonics

In this way, for the 4^{th}, 5^{th} …… modes of vibration in the stretched string the frequency

For the fifth, 5th….. Harmonics are emitted.

The general equation of frequency of wave in stretched string is given by,

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]]>The post Velocity of sound by resonance air column tube appeared first on Reference Notes.

]]>The experimental setup of resonance tube experiment to determine the velocity of sound in air is shown in figure, to find the velocity of sound in air the water level in the tube is brought close to the open end of the tube by changing the place of water reservoir. A tuning fork of frequency ‘f’ is set into vibration by striking it against the rubber pad and held it horizontal over the open end. The length of air column in the tube is increased by changing the position of reservoir in doing so, a condition is reached at which the sound heard is maximum, this condition is known as first resonance. If l1 be the first resonating length and l be the wave length of sound when,

If we go on increasing the length of air column in the tube the intensity of the sound heard goes on decreasing first become minimum and then again goes on increasing at a certain length. The intensity of sound becomes maximum again, these condition is called second resonating length.

If l_{2} be the second resonating length,

If U be the velocity of sound at room temperature.

Then,

Where j is the frequency of sound which is equal to frequency of turning fork,

Velocity of sound at NTP is given by

where, P-NTP = pressure at NTP

f = aqueous tension

r = cubical expansively of air = 1/273

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]]>The post End Correction appeared first on Reference Notes.

]]>According to the Rayleigh, “the end correction for the closed organ pipe is 0.3d and 0.6 d for the open organ pipe. Where d is the internal diameter of the pipe.”

If to be the first resonating length and be the wave length of the wave in the pipe then in first resonation,

Similarly if l_{2} be the second resonating length and be the wavelength of wave in the pipe, then,

Solving equation (i) and (ii), we get

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]]>The post Open organ pipe appeared first on Reference Notes.

]]>**Different modes of vibration in open pipe:**

In the mode of vibration in the organ pipe, two antinodes are formed at two open ends and one node is formed in between them. If length of the pipe be ‘l’ and be the wavelength of wave emitted in this mode of vibration. Then,

if ‘μ’ be the velocity of sound and to be the frequency of wave in this mode of vibration. Then,

This is the fundamental frequency of 1^{st} overtone or 2 harmonious.

In the second mode of vibration in the open organ pipe, there antinodes are formed at two ends and two nodes between them.

If ‘l’ be the length of the pipe and λ_{1} be the wavelength of wave emitted in this mode of vibration. Then,

If μ be the velocity of sound and to be the frequency of wave in this mode of vibration, then,

This is the fundamental frequency of 2^{nd} overtone or harmonics.

In the third mode of vibration in the open organ pipe, four antinodes are formed and three nodes between them. If ‘l’ be the length of the pipe and λ_{2} be the wavelength of wave emitted in this mode of vibration then

if μ be the velocity of sound and f_{2} be the frequency of wavelength on this mode of vibration, then,

This is the fundamental of 2^{nd} overtone & 3^{rd} harmonics.

In this way, for the 4^{th}, 5^{th} …………….. modes of vibration, the frequency of wave are f_{3 }= 4f_{0;} f_{4 }= 5f_{0}…………….are the frequency of 4^{th}, 5^{th} harmonics. Hence in open organ pipe odd and even both harmonic are present. Then the sound heard by open organ is so sonorous.

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]]>The post Closed organ pipe appeared first on Reference Notes.

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The different mode of the vibration in the closed organ pipe is discussed as below.

In the first mode of vibration in the closed organ pipe, an antinode is formed at the open end and a node is formed at the close end. If ‘l’ be the length of pipe and be the wavelength of wave emitted in this mode of vibration.

Then,

if ‘μ’ be the velocity of sound and to be the frequency of wave in this mode of vibration.

This is fundamental frequency of 1^{st} harmonics.

** **

In this mode of vibration two antinodes and two nodes are formed as in fig. If ‘λ’ be the length of pipe and be the wavelength of wave emitted in this mode of vibration. Then,

if μ be the velocity of wave and f_{1} be the frequency of wave, in this mode of vibration

This is the frequency of 1^{st} overtone of third harmonics.

** **In this mode of vibration three antinodes and three nodes are formed as in fig. If ‘l’ be the length of the pipe and be the wavelength of wave admitted in this mode of vibration. Then,

ff μ be the velocity of wave and f_{2} be the frequency of wave. If this mode of vibration,

f_{2} = 5f_{0}

This is the frequency of 2^{nd} overtone & firth harmonics.

In this way, for the 4^{th}, 5^{th}…. modes of vibration the frequency of wave emitted are 7f_{0}, 9f_{0}……. which are called 7^{th} , 9^{th} …… harmonics i.e. in the closed organ pipe only odd harmonic are present.

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