CBSE Class 10 Physics Waves and Sound Notes Set 19

Waves

A wave is a disturbance that moves through a medium or through space and carries energy from one place to another without any net movement of the medium. The particles of the medium only oscillate about their mean positions. Waves carry energy, momentum and the pattern of the disturbance.

1. Mechanical waves need a material medium (solid, liquid or gas). Sound, water waves and waves on a string are mechanical.
2. Non-mechanical (electromagnetic) waves need no medium and can travel through vacuum. Light is an example.
3. Transverse waves: particles vibrate at right angles to the direction of travel. They show crests and troughs and travel in solids and on liquid surfaces, with no change of pressure or density.
4. Longitudinal waves: particles vibrate along the direction of travel. They show compressions (high density, high pressure) and rarefactions (low density, low pressure) and travel in solids, liquids and gases.

Terms Used to Describe a Wave

Fundamental wave equation: \( v = f\lambda = \dfrac{\lambda}{T} \). The frequency is fixed by the source and does not change when the wave enters another medium; the speed and wavelength change. The distance between a crest and the next trough is \( \lambda/2 \).

Sound

Sound is produced by vibrating bodies and travels as a longitudinal mechanical wave, so it cannot travel through vacuum. The frequency of the sound equals the frequency of the source.

1. Speed of sound is greatest in solids, less in liquids and least in gases (air about 340 m/s, water about 1500 m/s, steel about 5000 m/s).
2. Speed increases with temperature (about proportional to \( \sqrt{T} \) in kelvin) and with humidity, since moist air is less dense. It is not changed by pressure, frequency or amplitude.
3. Lightning is seen before thunder is heard because light is far faster than sound.

Audible Range, Infrasound and Ultrasound

The human ear hears from 20 Hz to 20,000 Hz. Below 20 Hz is infrasound (used by elephants, rhinoceroses and produced by earthquakes). Above 20,000 Hz is ultrasound (used by bats, dolphins and in SONAR, medical scanning and industrial cleaning and flaw detection). A speed greater than the speed of sound is supersonic and produces a conical shock wave and a sonic boom.

Characteristics of Sound

A tone is a sound of a single frequency; a note is a mixture of frequencies that is pleasant to hear; noise is unpleasant.

Reflection of Sound, Echo and Reverberation

Sound reflects from hard surfaces following the same laws of reflection as light. An echo is the reflected sound heard separately from the original. The ear retains a sound for about 0.1 s, so the echo must arrive more than 0.1 s later. The minimum distance to the reflector is about \( \dfrac{340 \times 0.1}{2} = 17 \) m. Distance of the reflector = \( \dfrac{vt}{2} \).

Reverberation is the persistence of sound due to repeated reflections. It is reduced in halls by using sound-absorbing walls, curtains and carpets. Megaphones, horns and stethoscopes use reflection, and curved ceilings and soundboards spread sound over the hall. SONAR sends ultrasonic pulses and measures the time of return of the echo to find the depth of the sea or the position of submarines. Bats and dolphins use echolocation.

Human Ear

Sound is collected by the pinna and travels down the auditory canal to the eardrum, which vibrates. In the middle ear the three small bones (hammer, anvil and stirrup) amplify the vibrations and pass them to the cochlea of the inner ear, where hair cells convert them into electrical signals that the auditory nerve carries to the brain. The Eustachian tube equalises pressure on both sides of the eardrum.

Oscillations, Pendulum and Resonance

1. Simple pendulum: \( T = 2\pi\sqrt{l/g} \). The time period depends on the length and on g, not on the mass or the amplitude (small angles). A second's pendulum has T = 2 s and f = 0.5 Hz.
2. Free oscillations have a constant amplitude and a natural frequency. Damped oscillations lose amplitude because of air resistance and friction. Forced oscillations are driven by an external periodic force.
3. Resonance occurs when the driving frequency equals the natural frequency of the system, and the amplitude becomes very large. Soldiers break step on a bridge to avoid resonance; resonance is useful in tuning a radio and in musical instruments.
4. The frequency of a stretched string increases with tension and decreases with length and mass per unit length.

Worked Examples

Example 1. A wave has frequency 50 Hz and wavelength 6.8 m. Speed = 50 \( \times \) 6.8 = 340 m/s.

Example 2. A boy hears an echo 3 s after shouting. With v = 340 m/s, the reflector is at 340 \( \times \) 3/2 = 510 m.

Example 3. A pendulum of length 1 m on the Earth (g = 10 m/s\( ^2 \)) has T = 2\( \pi \sqrt{1/10} \) = 1.99 s, about 2 s.