Traveling Sound Waves

Concept: SONAR is a technology used primarily for underwater detection and navigation. It relies on sound waves. Step 1: Understanding SONAR SONAR is an acronym for SOund NAvigation and Ranging. It works by emitting sound pulses and then detecting the echoes that return after these pulses reflect off objects. By measuring the time delay between the emission of the pulse and the reception of the echo, the distance to the object can be determined. Step 2: Classifying Sound Waves by Frequency Sound waves are categorized based on their frequency:
Infra Sound (Infrasonic waves): Frequencies below the range of human hearing, typically less than .
Audible Sound: Frequencies within the range of human hearing, typically from to (or ).
Ultra Sound (Ultrasonic waves): Frequencies above the range of human hearing, typically greater than (or ). Note: "Radio Sound" is not a standard classification for sound waves used in this context. Radio waves are electromagnetic waves, not sound waves, and are used in RADAR, not typically SONAR. Step 3: Why Ultra Sound is Used in SONAR Ultrasonic waves are chosen for SONAR applications due to several advantageous properties:
High Frequency and Short Wavelength: Ultrasonic waves have high frequencies, which mean they have short wavelengths (since wavelength , where is the speed of sound and is frequency). Short wavelengths are less prone to diffraction (bending around obstacles) and can be focused into narrow beams. This allows for better resolution in detecting smaller objects and determining their direction more accurately.
Good Directionality: Because they can be directed in a narrow beam, they are not easily scattered in all directions. This is crucial for pinpointing the location of an object.
High Energy: Ultrasonic waves can be produced with high energy, allowing them to travel longer distances in water without significant loss of intensity. Audible sound waves have longer wavelengths and would spread out more, making it harder to detect small objects or determine their precise location. Infrasound has very long wavelengths and is generally not suitable for the detailed ranging and imaging tasks SONAR is used for. Therefore, Ultra Sound is the type of sound used in SONAR systems.

Concept: An echo is the repetition of sound caused by the reflection of sound waves from a surface. For an echo to be heard distinctly, there must be a minimum time interval between the original sound and the reflected sound. This minimum time interval is known as the persistence of hearing. Step 1: Persistence of Hearing The human ear can distinguish between two sounds if the time interval between them is at least about seconds. This is called the persistence of hearing. So, for an echo to be heard distinctly, the reflected sound must reach the ear at least seconds after the original sound is produced. Let . Step 2: Speed of Sound The speed of sound in air varies with temperature. At a room temperature of around to , the speed of sound is approximately . We will use this value for calculation, as it directly leads to one of the options. Let . Step 3: Calculating the Minimum Distance Let be the minimum distance between the source of sound and the reflecting surface. For an echo, the sound travels from the source to the reflecting surface (distance ) and then travels back from the reflecting surface to the source/listener (another distance ). So, the total distance travelled by the sound for the echo to be heard is . We know the basic relationship: distance = speed × time. Applying this to our echo scenario: To find the minimum distance to the reflector, we can rearrange the formula: Step 4: Substitution and Calculation Substitute the values of and into the formula: Thus, the minimum distance between the source and the reflecting surface for an echo to be heard distinctly is .

Concept: Time period and frequency are fundamental properties of periodic phenomena like waves or oscillations. They are inversely related. Step 1: Understanding Time Period (T) The time period ( ) is the time taken for one complete cycle of a wave or one full oscillation. Given: Time period . Step 2: Understanding Frequency (f) Frequency ( ) is the number of complete cycles or oscillations that occur in one second. The unit of frequency is Hertz (Hz), where . Step 3: The Relationship between Frequency and Time Period Frequency and time period are reciprocals of each other. The formula connecting them is: This means that if you know the time period, you can calculate the frequency, and vice-versa ( ). Step 4: Calculation We are given . Substitute this value into the frequency formula: To simplify the division by a decimal, you can express as a fraction: . So the equation becomes: When dividing by a fraction, you multiply by its reciprocal: Therefore, if the time period is seconds, the frequency will be .

Step 1: Understand the Nature of Sound Waves.
Sound is a mechanical wave that requires a medium to propagate. It can travel through: 1. Solids:
Sound travels fastest in solids due to their high density and strong intermolecular forces. 2. Liquids:
Sound travels slower in liquids compared to solids but faster than in gases due to the intermediate density and molecular interactions. 3. Vacuum:
Sound cannot travel through a vacuum because there are no particles to transmit the wave. A vacuum lacks the medium necessary for sound propagation. Step 2: Analyze Each Option.
Option (1): Solid — Incorrect, as sound can also travel through liquids.
Option (2): Liquid — Incorrect, as sound can also travel through solids.
Option (3): Vacuum — Incorrect, as sound cannot travel through a vacuum.
Option (4): 1 and 2 both — Correct, as sound can travel through both solids and liquids. Step 3: Final Answer. $ $

Step 1: Recall the Relationship Between Velocity, Frequency, and Wavelength.
The relationship between the velocity ( ), frequency ( ), and wavelength ( ) of a wave is given by: This equation can be rearranged to express frequency or wavelength in terms of the other variables: Step 2: Analyze Each Option.
Option (1): — Correct, as this is the standard wave equation.
Option (2): — Correct, as this is a valid rearrangement of the wave equation.
Option (3): — Correct, as this is another valid rearrangement of the wave equation.
Option (4): All of these — Correct, as all three equations are valid relationships derived from the wave equation. Step 3: Final Answer.