Notes-Part-2-Class-11-Science-Physics-Chapter-8-Sound-Maharashtra Board

Topics to be Learn : Part-1 Types of waves Common properties of all waves Transverse waves and longitudinal waves Speed of travelling waves Principle of superposition of waves Topics to be Learn : Part-2 Echo, reverberation and acoustics Qualities of sound Doppler effect

Echo, reverberation and acoustics:

Sound waves obey the same laws of reflection as those of light.

Echo : An echo is the repetition of the original sound because of reflection from some rigid surface at a distance from the source of sound.

• If we clap or shout in a hilly region or near a suitable reflecting medium, we are likely to hear an echo after some time interval.
• Echoes may be heard more than once due to multiple reflection of sound but a true echo is a single reflection of the first original sound.

Important factors for a distinct echo :

To hear an echo distinctly,

• The reflected sound must reach the listener after at least 0.1 s, as the sensation of sound lasts in our brain for about 0.1 s
• The minimum distance between the source and reflecting medium must be 17.2 m (assuming that the speed of sound in air is 344 m/s).
• The speed of sound in air increases with a rise in temperature of air. Hence, the minimum distance required for hearing distinct echo, increases with a rise

Reason : why we cannot hear an echo at every place :

• The minimum distance between the source of sound and the reflecting surface should be 17.2 m to hear a recognisable echo (at 22 °C), since the time delay between the original sound and the reflected sound should be at least 0.1 s. This criteria is often not met anywhere. As a result, we cannot hear an echo everywhere.

Reverberation:

• The persistence of sound due to repeated reflections from the walls, ceiling and other surfaces is called reverberation.
• If the distance between the reflecting surface of a closed space and the source of sound is less than 17 m, the sound waves get reflected many times. Due to this the original sound seems to be prolonged.
• If the reverberation is too long, the sound cannot be heard clearly due to overlapping of reflected waves and direct waves produced by the source after the production of earlier waves.

Methods to decrease reverberation :

• To avoid these problems, reverberation should be decreased.
• For this the roof and walls of the auditorium are covered with sound absorbent materials such as compressed fibre board.
• Thick curtains being good absorbers of sound are put on doors and windows. Similarly carpets are put on the floor.
• Seats in an auditorium are made using the material having sound absorbing properties to reduce reverberation.
• Porous cardboard sheets, perforated acoustic tiles, gypsum boards, thick curtains etc. at the ceilings and at the walls are most convenient to reduce reverberation.

Acoustics:

The branch of physics which deals with the study of production, transmission and reception of sound is called acoustics.

Conditions that must be satisfied for proper acoustics in an auditorium :

• Sound should be heard loud and clear at all points in the auditorium. This can be achieved by keeping a parabolic surface behind the speaker, with the speaker at its focus. This causes the sound, after reflection from the surface, to spread uniformly across the width of the auditorium. Due to this, good loudness is maintained through the entire auditorium.
• Echoes and reverberation must be eliminated or reduced. Echoes can be reduced by making the reflecting surfaces more absorptive. Echo will be less if the auditorium is full.
• Unnecessary focusing of sound should be avoided and there should not be any zone of poor audibility or region of silence. For that purpose curved surface of the wall or ceiling should be avoided.
• Echelon effect : It is due to the mixing of sound produced in the hall by the echoes of sound produced in front of regular structure like the stairs. To avoid this, stair type construction must be avoided in the hall.
• The auditorium should be sound-proof when closed, so that stray sound cannot enter from outside.
• For proper acoustics no sound should be produced from the inside fittings, seats, etc. Instead of fans, air conditioners may be used. Soft action door closers should be used.

Qualities of sound:

Major qualities or characteristics of sound are (i) Pitch, (ii) Timbre or quality and (iii) Loudness.

(i) Pitch: By pitch we mean whether the note is high or low. The pitch of a note depends upon the frequency of the sound. But pitch is not determined by frequency alone. A physiological factor is involved and the sense of pitch is modified by the loudness and quality of the sound.

• The average range of frequencies that the human ear detects as sound is approximately 20 Hz to 20000 Hz (the audible range).
• The human ear is capable of detecting a difference in pitch between two notes.
• The frequency of sound determines its pitch. A high pitched or shrill sound is produced by a body vibrating with a high frequency and a low pitched or flat sound is produced by a body vibrating with a low frequency.
• The smallest difference in frequency that the ear can detect as a difference in pitch is approximately proportional to the frequency of one of the notes.
• That is, a given change in frequency of a low note will produce a greater change in pitch than it will in a high note.

(ii) Quality:

The property of a sound that allows it to be identified from all other sounds of the same pitch and volume is referred to as the quality or timbre.

The same note performed at the same volume on two distinct musical instruments may be clearly distinguished from one another by their timbre.

• Example : The quality or timbre of the sound of a sitar is different from that of a guitar. The number of overtones or partials present and their relative intensities determine the quality or timbre of the sound of a musical instrument. Therefore, even if the pitch and the loudness are the same, the notes of a sitar and a guitar sound different.

(iii) Loudness : The loudness of a note is the magnitude of the sensation produced by the sound waves on the ear.

It depends upon

• The energy of the vibration, the sensitiveness of the individual ear, the pitch of the sound.
• The loudness of a sound depends on the intensity of the sound wave, which is in turn proportional to the square of the amplitude of the wave itself.
• Loudness is a physiological (subjective) sensation, while intensity is an objectively measurable physical property of the wave.
• There is no direct relation between loudness and intensity.
• Near the middle of the audible range of frequencies, the ear is very sensitive to changes in intensity, which it interprets as changes in loudness.

Intensity of sound : The intensity of sound at a point is the time rate of flow of sound energy passing normally through a unit area at that point.

• Its unit is the joule per second square metre (J/s.m²) ≡ watt per square metre (W/m²).
• Intensity and loudness are related, but not the same. Intensity is a measurable quantity whereas loudness is a sensation which is not measurable.
• Loudness depends on the intensity of sound as well as the sensitivity of the ear of the listener.

Decibel : The decibel is a unit used to compare, usually, two sound intensity levels. If l is the level of sound intensity to be measured that differs from a reference level I₀ by β decibels.

β = 10 log₁₀ \(\frac{I}{I_0}\)            ….(in decibels)

=  log₁₀ \(\frac{I}{I_0}\)                …..(in bels)

I₀ is usually the intensity of a note of the same frequency at the threshold of audibility.

• One decibel represents an increase in intensity of about 26 per cent (for l = 1.259 I₀, log₁₀259 = 0.1).
• Ten such increases involve an increase of intensity to (1.26)¹⁰ times the original intensity, approximately a tenfold increase called a bel.
• The decibel is one-tenth of a bel, but it is the decibel (not the bel) which is invariable used because one decibel is about the smallest change the ear can easily detect under normal conditions.
• The decibel or bel is not a unit of loudness.

Q. Explain why using earphones for a long time is not advisable.

Doppler Effect:

The apparent change in the frequency of sound heard by a listener, due to the relative motion of the source of sound and the listener, is called the Doppler effect in sound.

Explanation :

• The amount of sound waves that are transmitted to a listener per unit time increases when a sound source gets closer to a listener who is standing still. As a result, the listener perceives a sound frequency that is higher than the actual sound frequency. This effect is also observed when (i) the listener moves towards a stationary source of sound or (ii) both the source and the listener move towards each other.
• If a source of sound moves away from a stationary listener, there is a decrease in the number of sound waves reaching the listener per unit time. Consequently, the apparent frequency of sound heard by the listener is less than the true frequency of sound. This effect is also observed when (i) the listener moves away from a stationary source of sound or (ii) both the source and the listener move away from each other.
• The apparent change in frequency, called the Doppler shift, depends on the velocities of (i) sound, (ii) listener and (iii) the source of sound.

Expression for the apparent frequency of sound heard when the source of sound is moving away (receding) from the stationary listener.

Consider a source of sound S as it moves away from a stationary listener L with a speed v_s. Suppose that the intervening medium (air) is at rest, i.e., there is no wind. Let v_s speed of sound in still air. If n₀ and T₀ be the frequency and period of the sound note emitted by S,

n₀ = \(\frac{1}{T_0}\)

Suppose the source emits a crest when it is at S₁, at time t = 0.

If S₁L = d, this crest reaches L at time

t₁ = d/v          …..(1)

The next crest is emitted by S when it is at S₂ at time t = T_0. S₂L = S₁L + S₁S₂ = d + v_sT₀. This second crest then reaches L at time

t₂ = T₀ + \([\frac{d+v_sT_0}{v}]\)         …..(2)

In general, the (p+1)^th crest reaches L at time,

t_p+1 = pT₀ + \([\frac{d+pv_sT_0}{v}]\)          …..(3)

where p is a positive integer.

From Eqs. (1) and (3), the time interval for counting p crests is,

t_p+1 — t₁ = pT₀ + \([\frac{pv_sT_0}{v}]-\frac{d}{v}\)

= pT₀ + \(\frac{d}{v}+\frac{pv_sT_0}{v}]-\frac{d}{v}\)

= pT₀ \((1+\frac{v_s}{v})\)

∴  \(\frac{t_{p+1}-t_1}{p}\) =  T₀ \((1+\frac{v_s}{v})\)         …..(4)

The LHS of Eq. (4) is the period (T) of the sound wave apparent to the listener.

∴ T = T₀ \([\frac{v+v_s}{v}]\)

∴ \(\frac{1}{T}=\frac{1}{T_0}[\frac{v}{v+v_s}]\)

Now 1/T = n ≡ the apparent frequency of the sound.

n = n₀ \([\frac{v}{v+v_s}]\)             …..(5)

n₀ ≡ actual frequency of sound

v ≡ speed of sound in air and

v_s ≡ speed of the source of sound

(i) The apparent frequency when the source is moving towards (approaching) the stationary listener is

n = n₀ \([\frac{v}{v-v_s}]\)

Expression for the apparent frequency of sound heard when the listener is moving towards (approaching) a stationary source :

Consider a listener L moving towards a stationary source of sound S with a speed v_L.

Suppose the intervening medium (air) is at rest, i.e., there is no wind. Let v_s ≡ speed of sound in still air. If n₀ and T₀ be the frequency and period of the sound note emitted by S,

n₀ = \(\frac{1}{T_0}\)

L₁ = Position of listener at t = 0,

L₂ = Position of listener at t = t₁,

L₃ = Position of listener at t = t₂,

S = Position of stationary sound source of period T₀,

v_L = Speed of listener, v =Speed of sound in still air

Suppose at time t=0, the source is at a distance d from the listener at L₁, when it emits the first crest. The crest reaches the listener at time t₁ during which the listener covers a distance v_L t₁ towards the source and reaches point L₂.

Also, in this time t₁, the distance covered by the sound wave is

vt₁ = d — v_Lt₁

∴ vt₁ + v_Lt₁ = d

∴ t₁ = \(\frac{d}{v+v_L}\)          ….(1)

At time t = T₀, the source emits the second crest which reaches the listener at instant t₂. In time t₂, the listener covers a distance v_Lt₂ towards the source and reaches point L₃. In the time t₂ — T₀, the distance covered by the sound wave is

SL₃ = v(t₂ — T₀) = d — v_Lt₂

∴ t₂(v + v_L) = d + vT₀

∴ t₂ = \(\frac{d+vT_0}{v+v_L}\)            ….(2)

Similarly, for the (p + 1)th crest,

t_p+1 = \(\frac{d+pvT_0}{v+v_L}\)           ….(3)

where p is a positive integer.

From Eqs. (1) and (2), we get,

t_p+1 — t₁ = \(\frac{d+pvT_0}{v+v_L}-\frac{d}{v+v_L}\) = \(\frac{pvT_0}{v+v_L}\)

∴ T = \(\frac{t_{p+1}-t_1}{p}\) = \(\frac{vT_0}{v+v_L}\)         ….(4)

where T is the period of sound apparent to the listener.

∴ \(\frac{1}{T}=\frac{1}{T_0}[\frac{v+v_L}{v}]\)

Now, \(\frac{1}{T}\) = n, = the apparent frequency of sound.

∴ n = n₀ \(\frac{v+v_L}{v}\)     …..(5)

n₀ ≡ actual frequency of sound

(i) The apparent frequency when the listener is moving away (receding) from the stationary source is :

n = n₀ \(\frac{v-v_L}{v}\)

(ii) For the source and listener moving towards (approaching) each other :

n = n₀ \(\frac{v+v_L}{v-v_s}\) 

(iii) For the source and listener moving away (receding) from each other :

n = n₀ \(\frac{v-v_L}{v+v_s}\)

(iv) The apparent frequency of sound heard when the listener and source are moving with the same speed along the same direction :

• In this case, the apparent frequency equals the actual frequency as there is no relative motion.

Conclusion :

• If |v_L| = |v_s|, n = n₀. Thus there is no Doppler shift as there is no relative motion, even if both are moving.
• If |v_L| > |v_s|, numerator will be greater, n > n₀. This is because there is relative approach as the listener approaches the source faster and the source is receding at a slower rate.
• If |v_L| < |v_s|, n < n₀ as now there is relative recede (source recedes faster, listener approaches slowly).

Common Properties between Doppler Effect of Sound and Light:

• When a listener (or observer) and a source (of sound or light) are in relative motion, the apparent and emitted frequencies are different.
• If the relative motion of the listener (or observer) and the source (of sound or light) is towards each other, the apparent frequency is higher than the emitted frequency.
• If the relative motion of the listener (or observer) and the source (of sound or light) is away from each other, the apparent frequency is lower than the emitted frequency.
• If v_L or vs are much smaller than that of the speed of sound or light, the relative velocity v_r can be used. Then, the expression for the apparent frequency is,

n = n₀ \([1±\frac{v_r}{v}]\)

• Here, the upper sign is used during relative approach whereas the lower sign is used during relative recede.
• When the velocities of source and observer (listener) are not along the same line, their respective components along the line joining them should be considered for longitudinal Doppler effect.

Major Differences between Doppler Effects of Sound and Light:

• No matter who is moving, only the relative velocity between the observer and the source is relevant for the Doppler shift in the frequency of light waves. The perceived frequency of sound, however, is dependent on whether the observer or the source is moving.
• The effects of Doppler in light, both classical and relativistic, differ. The only type of sound is classical.
• The velocity of wind changes the speed of sound, in turn affecting the Doppler shift. In this case, the component of wind velocity along the line joining the source and observer, v_w is algebraically added to the velocity of sound. That is, the velocity of sound in still air (v) must be replaced with v + v_w. Since v is directed from the source to listener, the plus sign must be considered if v_w is toward the listener and the minus sign must be used if v_w is toward the source.