Sound

Assertion is true but reason is false

Explanation

Assertion (A) is true because to increase the pitch (or make the sound shrill) in a flute, the holes are opened so as to reduce the length of the vibrating air column.

Reason (R) is false because in a flute, holes are opened to reduce the length of the vibrating air column and vice versa.

Both A and R are true and R is the correct explanation of A

Explanation

Assertion (A) is true because loudness and quality (or timbre) of sound are independent properties and changing one does not necessarily affect the other.

Reason (R) is true because loudness depends on the amplitude of the sound wave such that greater amplitude means louder sound and quality depends on the waveform or the shape of the sound wave, which is influenced by the mixture of frequencies.

So here reason correctly explains why the loudness and the quality of sound are independent of each other.

(a) The time period of a wave is 2 s. Its frequency is 0.5 hertz.

(b) The pitch of a stringed instrument is increased by increasing tension in string.

(c) The pitch of a flute is decreased by increasing length of air column.

(d) Smaller the membrane, higher is the pitch.

(e) If a drum is beaten hard, its loudness increases.

(f) A tuning fork produces sound of single frequency.

When a source of sound vibrates, it creates a periodic disturbance in the medium near it. The disturbance then travels in the medium in the form of waves. This can be understood by the following example —

Take a thin metal strip. Keeping it vertical, fix it's lower end. Push it's upper end to one side and then release it. As it vibrates (i.e., moves alternatively to the right and left) sound is heard.

When the strip advances to the right from a to b, it pushes the particles of air in layers in front of it. So the particles of air in these layers gets closer to each other i.e., air of these layers gets compressed.

The particles of these layers while moving forward, push and compress the layers next to them, which then compress the next layers and so on. Thus, the disturbance moves forward in form of compression. The particles of the medium get displaced, but they do not move along with the compression.

As the metal strip starts returning from b to a as shown in figure, after pushing the particles in front, the particles of air near the strip starts returning back to their mean positions due to the elasticity of the medium.

When the strip moves to the left from a to c, it pushes back the layers of air near it towards it's left and thus produces a space of very low pressure on it's right side. The air layers on the right side of the strip expand in this region thus forming the rarefied air layers. This region of low pressure is called the rarefaction R.

When the strip returns from c to it's normal position a, it pushes the rarefaction R forward and the air layers near the strip again pass through their mean positions due to the elasticity of the medium.

In this manner, as the strip moves to the right and left repeatedly, the compressions and rarefactions regions are produced one after the other which carry the disturbance with it with a definite speed depending on the nature of the medium. Gradually due to friction, the strip losses its energy to the medium and the disturbance dies out.

One complete to and fro motion of the strip forms one compression and one rarefaction which together constitute one longitudinal wave. This is how sound waves propagate through the formation of a longitudinal wave when source vibrates in air.

Loudness is the characteristic by virtue of which a loud sound can be distinguished from a faint one, both having the same pitch and quality.

The figure below shows how a wave pattern of a loud note differ from the soft note.

Pitch of sound enables to distinguish two sounds of same loudness, but of different frequencies, given by the same instrument.
Pitch is the characteristic of sound which distinguishes a shrill sound from a flat sound. Pitch of a sound depends on the frequency of the vibrating body.

Wave patterns of high pitch note and low pitch note of the same loudness are shown in the diagram below:

(i) Loudness (L) ∝ [amplitude (a)]²

Ratio of loudness =

$\dfrac{\text{L}_1}{\text{L}_2} = \dfrac{(\text{a}_1)^2}{(\text{a}_2)^2} = \dfrac{(1)^2}{(3)^2} = \dfrac{1}{9}$

So L₁ : L₂ = 1 : 9.

(ii) Frequency remains the same if the pitch remains unchanged.

$\dfrac{\text{pitch of 1st wave}}{\text{pitch of 2nd wave}} = \dfrac{\text{1}}{\text{1}} = 1:1$

So pitch will be 1 : 1.

(i) Since amplitude of two waves are same so loudness of both the waves will be same.

$\dfrac{\text{amplitude of 1st wave}}{\text{amplitude of 2nd wave}} = \dfrac{\text{1}}{\text{1}} = 1:1$

So, loudness of first wave : loudness of second wave = 1:1.

(ii) Frequency determines the pitch of the sound.

$\dfrac{\text{frequency of 1st wave}}{\text{frequency of 2nd wave}} = \dfrac{\text{256}}{\text{512}} = \dfrac{\text{1}}{\text{2}} = 1:2$

So pitch of first wave : pitch of second wave = 1 : 2.

In figure (a) the amplitude of wave A is 2 m and in figure (b) the amplitude of wave B is 4 m. But both the waves have same frequency (pitch).

Ratio of amplitude of wave A to wave B = 2 : 4 = 1 : 2.

The two waves with frequencies 256 Hz and 512 Hz are represented in graphical form below :

vacuum

Reason — Sound needs a medium for its propagation. It cannot travel in vacuum.

the particles of medium transfer energy without leaving their mean positions.

Reason — Sound travels in air in form of longitudinal waves. The particles of the medium vibrate about their mean positions and transfer energy with a constant speed from one place of medium to another place during propagation of wave.

0 to 80 dB

Reason — The safe limit of level of sound for hearing is from 0 to 80 dB.

decibel

Reason — The unit of loudness of sound is decibel.

using thicker string

Reason — In stringed instruments like piano, a note of lower pitch can be obtained by vibrating the string under low tension or by vibrating a thicker string.

loudness decreases

Reason — Loudness is proportional to the square of the amplitude i.e.,

Loudness ∝ (amplitude)²

So, when a body vibrates with a lesser amplitude, it sends forth a smaller amount of energy.

Hence, the energy received by the ear drum is also small, so the loudness of the sound decreases.

frequency

Reason — The pitch of a sound depends on the frequency of the vibrating body. A sound of high frequency is said to have a high pitch, while a sound of low frequency is said to have a low pitch.

Sound travels in air in form of longitudinal waves. When a body vibrates, it creates a periodic disturbance in air. The disturbance then travels in air in the form of waves.

The wave in which the particles of the medium vibrate about their mean positions, in the direction of propagation of sound is called longitudinal wave.

(a) Amplitude (a) — The maximum displacement of a particle of medium on either side of its mean position, is called the amplitude of wave.

(b) Frequency (f) — The number of vibrations produced by a particle of the medium in one second is called the frequency of the wave.

(c) Time period (T) — The time taken by a particle of medium to complete its one vibration is called the time period of the wave.

If T is the time period of a wave, then by definition

In time T, the number of waves = 1

∴ In 1 second, number of waves (or frequency) =

$\text f = \dfrac{\text{1}}{\text{T}}$

Thus,

$\text{frequency} = \dfrac{\text{1}}{\text{Time period}}$

or

$\text{time period} = \dfrac{\text{1}}{\text{frequency}}$

The three characteristics of a musical sound are:

1. Loudness
2. Pitch (or shrillness) and
3. Quality (or timbre or wave form).

Amplitude determines the loudness of a sound wave.

Loudness is directly proportional to the square of amplitude of wave.

Loudness ∝ (amplitude)²

Hence, greater the amplitude of vibrations, louder is the sound produced.

The loudness (L) of a sound is directly proportional to the square of amplitude of wave.

Loudness ∝ (amplitude)²

L = (2)² = 4 times.

So, if the amplitude (a) of a wave is doubled, loudness will be four times.

The unit in which loudness of sound is expressed is decibel (dB).

Larger the surface area of the vibrating body, louder is the sound heard as a large vibrating area sends forth a greater amount of energy. By mounting a wire on a sound board, the surface area increases which in turn increases the loudness of the sound produced.

The three factors on which loudness of sound heard by a listener depends are:

1. Amplitude of wave.
2. Distance of source of the sound.
3. Surface area of the vibrating body.

Frequency determines the pitch of a sound. Higher the frequency, higher is the pitch and sound produced is shrill. Lower the frequency, lower is the pitch and sound produced is flat.

The characteristic of sound related to its frequency is pitch.

Timbre or quality of sound makes it possible to recognize a person by his voice without seeing him. The vibrations produced by the vocal cord of each person have a characteristic wave form which is different for different persons.

(a) Frequency determines the pitch of a note.

(b) Amplitude determines the loudness of the sound heard.

(c) Wave form determines the quality of the note.

(a) Loudness.

(b) Quality.

(c) Pitch.

(a) Pitch of sound will be higher if a thin wire is used in a guitar.
Thin wires in stringed musical instruments produce sound with higher frequency and hence higher pitch.

(b) Pitch of sound will be low if a wire under less tension is used in guitar.
In stringed musical instruments, wires under less tension produce sound with lower frequency and hence lower pitch.

As the bucket fills up with water, the length of air column decreases, so the frequency of sound produced increases. Pitch or shrillness of sound will increase with increase in frequency of sound. So with increase in shrillness of sound we can detect the filling of a bucket under water tap.

Trumpet has the highest pitch because it has the highest frequency i.e. 500 Hz.

Pitch of a sound depends on its frequency. More the frequency of the note, higher is its pitch.

Jar B will produce sound of higher pitch when air is blown in it because jar B has less air column above water. Frequency of sound produced increases with decrease in the length of air column. Pitch or shrillness of sound increases with increase in frequency of sound.

When two identical guitars are played by two persons to give notes of the same loudness and pitch then they will not differ in quality as the identical guitars will produce identical wave forms.

Quality of a musical instrument depends on the number of subsidiary notes and their relative amplitudes present in it along with the principal note.

As same instruments produce same principal and subsidiary notes. Hence, the quality of identical guitars will be same.

(a) Loudness will be same for both the instruments because they have same amplitude.

(b) Pitch will be same for both the instruments as they have same frequencies.

(c) Quality will be different as they have different wave forms as seen in the diagram of the given wave patterns.

(a) Note from a musical instrument is shown by figure (d) because the sound produced by the musical instruments comprises of different frequencies and amplitudes resulting in a mixed type of wave form.

(b) Soft note is shown by figure (a) because this wave has low amplitude.

(c) Shrill note is shown by figure (c) because this wave has high frequency.

When a lighted candle is placed in front of a loudspeaker producing a loud and steady noise, the flame of the candle flickers.
A loudspeaker produces sound waves, which are longitudinal pressure waves in the air. These waves consist of alternating regions of compression and rarefaction that move outward from the speaker, causing the air near the loudspeaker to vibrate rapidly back and forth. The resulting air currents disturb the flame, making it flicker in step with the pressure variations of the sound waves.

(a) False
Correct Statement — When sound propagates in air, it carries energy with it.

(b) True

(c) False
Correct Statement — The distance between two consecutive compressions or between two consecutive rarefactions is equal to one wavelength.

(d) False
Correct Statement — The frequency is measured in hertz.

(e) False
Correct Statement — The quality of a sound depends on the wave form.

(f) True

(g) False
Correct Statement — Decibel is the unit of loudness of a sound.