Sound

(a) Wavelength

Figure: Wavelength of sound wave¹⁴

Distance between two consecutive compressions or rarefaction or two peak of a wave is called Wavelength. Wavelength is represented by Greek Letter "λ (Lambda)".

The SI unit of wavelength is meter (m) .

(b) Frequency

Frequency is the number of an event takes place in unit time.

When sound propagates through a medium, the density of the medium oscillates between a maximum value and a minimum value. The change in density from the maximum value to the minimum value, again to the maximum value, makes one complete oscillation.

The number of oscillations per unit time is called the Frequency of the sound wave.

The Frequency is generally denoted by Greek Letter "ν (Nu)". Sometimes frequency is denoted by English letter "f".

The SI unit of Frequency is hertz. Hertz is denoted by symbol "Hz".

(c) Time Period

The time taken by two consecutive compressions or rarefactions to cross a fixed point is called the Time Period of the wave.

In other words, time taken for one complete oscillation in the density of the medium is called the Time Period of the Sound wave.

Time Period is denoted by English letter "T".

The SI unit of Time Period is second (s).

Relation between Frequency and Time period

Frequency = 1/Time Period

`=>nu = 1/T`

(d) Amplitude

The magnitude of the maximum disturbance in the medium on either side of the mean value is called The Amplitude of the wave.

Figure: Amplitude of sound wave¹⁴

The amplitude is generally represented by letter "A".

Loudness and Softness of Sound Wave

The loudness or softness of a sound is determined by its Amplitude.

Amplitude is energy of a sound wave.

The amplitude of the sound wave depends upon the force with which an object is made to vibrate.

Example: If one strikes a table lightly this will produce soft sound because a sound wave of less energy (amplitude) is produced by striking table lightly.

Figure: Perception of Loudness of Sound wave¹⁵

Reference: By Rburtonresearch [CC BY-SA 4.0 ], from Wikimedia Commons

On the other hand if one hits the table hard, a loud sound is produced. This is because a sound wave of high energy (amplitude) is produced by hitting table strongly.

Figure: Wave of soft sound¹⁶

Loud sound because of associated with higher energy travel a larger distance and soft sound travel a shorter distance as it is associated with lesser energy.

Figure: Wave of louder sound¹⁷

A sound wave spreads out from its source. As it moves away from the source its amplitude, i.e. energy, as well as its loudness decreases.

(e) Pitch

Pitch is a characteristic of sound because of which we can distinguish among different melodies, i.e. music.

How the brain interprets the frequency of an emitted sound is called its Pitch. The faster the vibration of the source, the higher is the frequency and the higher is the pitch.

Objects of different sizes and conditions vibrate at different frequencies to produce sound of different pitch.

It is the pitch because of which we can differentiate between sound coming from a flute and a violin at the same time.

(f) Quality or Timber of sound

Quality or Timber of sound is one of the characteristics of sound that enables us to distinguish one sound from another having same pitch and loudness.

The sound which is more pleasant is said to be a rich quality. A sound of single frequency is called a tone.

Pleasant and Unpleasant Sound

The sound which is produced due to a mixture of several frequencies is called a note and is pleasant to listen to. Noise is unpleasant to the ear. Music is pleasant to hear and is of rich quality.

Example

Sound coming from a musical instrument playing by a trained musician is pleasant sound. Whereas, sound coming from the horn of a truck is unpleasant sound.

(g) Speed of Sound

The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travel per unit time.

In other words, speed of sound (v) is the distance travel by sound per unit time.

We know that, Speed (v) = distance / time

Thus, speed of sound (v) `=lambda/T`

Here, λ is the wavelength of the sound wave. It is the distance travelled by the sound wave in one time period (T) of the wave.

And, since, `nu=1/T`

Where, ν (nu) = frequency

Thus, speed of sound (v) `=lambda\ nu`

Thus, speed of sound = wavelength &215; frequency

The speed of sound remains almost the same for all frequencies in a given medium under the same physical conditions.

Example Problem (1) Find the speed of a sound wave of 5 kHz frequency and wavelength of 20 cm.

Solution :

Given, Frequency (ν) = 5 kHz = 5 × 1000 = 5000 Hz

Wavelength (λ) = 20 cm = 20/100 = 0.2 m

Thus, speed (v) = ?

We know that, speed of sound (v) = Wavelength × Frequency

⇒ speed (v) = 0.2 m × 5000 Hz

⇒ speed (v) = 1000 m/s

Thus, speed of sound is 1000 m/s Answer

Example Problem (2) In how much time a sound of 500 Hz and wavelength of 50 cm will reach at a distance of 1 km.

Solution :

Given, Frequency (ν) = 500 Hz

Wavelenght (&lambada;) = 50 cm = 50/100 = 0.5 m

Distance = 1 km = 1000 m

Thus, time to reach the given distance = ?

We know that,

Speed of sound (v) = Wavelength × Frequency

= 0.5 m × 500 Hz

⇒ Speed (v) = 250 m/s

Now,

∵ In reaching of 250 m it takes 1 second

∴ In reaching of 1 m time taken = 1/250 second

∴ In reaching of 1000 m time taken `= 1/250xx1000\ s`

Time required = 4 second. Answer

Thus, sound of given frequency and wavelength will take 4 second to reach the given distance of 1 km.

(h) Intensity of Sound

The amount of sound energy passing each second through unit area is called the Intensity of Sound.

Sometimes "Loudness" and "Intensity" are used in the same sense, but they are not same.

Loudness is a measure of the response of the ear to the sound.

Even when two sounds are of equal intensity, one may hear one as louder than the other simply because our ear detects it better.

Speed of Sound In Different Media

Sound propagates through a medium at a finite speed. The speed of sound is highest in solid, and lowest in gas among solid, liquid and gas.

When we go from solid to gasesous state, the speed of sound decreases and vice versa.

Variation of Speed of sound with Temperature

Speed of sound increases with increase in temperature and decrease with decrease in temperature in a particular medium. This is the cause; that we hear a sound more clearly in summer than in winter.

Example: Speed of sound in air is 331 m s^–1 at O⁰ C and 344 ms^–1 at 22⁰C.

Reflection of Sound

Bouncing back of sound from a solid or liquid is called Reflection of Sound. Sound bounces off similar to light or a rubber ball from a surface.

Reflection of sound follows the rule similar to light. This means sound also follows the Law of Reflection of light.

The directions in which the sound is incident and is reflected make equal angles with the normal to the reflecting surface at the point of incidence, and the three are in the same place.

An obstacle of large size which may be polished or rough is needed for the reflection of sound waves.

Echo

Reaching of sound after a delay to the listener because of bouncing back from a reflecting surface after the direct sound is called Echo or Echo of sound.

If we shout or clap near a tall building or a mountain or in a big hall, we hear the same sound again a little latter. This sound which we hear is called Echo.

This happens because, shouting or clapping sound bounces back to us after reflecting from the building, or mountain, or wall of big hall.

Successive or Multiple Reflection of Sound

The echo may be heard more than once because of successive or multiple reflection or sound.

In other words, the coming of sound to listener more than once after bouncing back from a reflecting surface is called Successive or Multiple Reflection of Sound.

The rolling of thunder is due to the successive reflection of sound from a number of reflecting surfaces, such as the clouds and the land.

Condition to hear an Echo

The sensation of sound persists in our brain for about 0.1 s. Thus, to hear a distinct echo the time interval between the original sound and the reflected one must be at least 0.1 s.

At 20⁰C, the speed of sound in air = 344 m/s

Thus, the sound must go to the obstacle and reach back to the ear of the listener on reflection after 0.1s.

Thus, the total distance covered by the sound from the point of generation to the reflecting surface and back should be at least (344 m/s) × 0.1 s = 34.4 m

Thus, for hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be half of the distance that is 34.4 m/2 = 17.2 m

Thus, distance of obstacle to hear a distinct echo must be at least 17.2 from the source of sound.