Waves

Concept: The relationship between the speed of a wave ( ), its frequency ( ), and its wavelength ( ) is given by . Also, time taken ( ) to travel a distance ( ) with a constant speed ( ) is given by . Step 1: Convert given quantities to SI units
Frequency ( ): 2 KHz (kilohertz) So, (or ).
Wavelength ( ): 35 cm (centimeters) So, .
Distance to travel ( ): 7 km (kilometers) So, . Step 2: Calculate the speed of the sound wave ( ) Using the formula : Step 3: Calculate the time taken to travel the given distance Using the formula : Distance Speed The time taken by the sound wave to travel 7 km is 10 seconds. This matches option (4).

Concept: The speed of sound varies depending on the medium through which it travels and factors like temperature, pressure, and salinity (for water). Sound generally travels faster in liquids and solids than in gases. Step 1: Factors Affecting Speed of Sound in Water In water, the speed of sound is primarily affected by:
Temperature: Speed increases with increasing temperature.
Salinity (salt content): Speed increases with increasing salinity. This is particularly relevant for seawater.
Pressure (Depth): Speed increases with increasing pressure (and thus depth). Step 2: Typical Values for Speed of Sound
In Air (at ): Approximately .
In Fresh Water (at ): Approximately .
In Sea Water: Due to salinity and typically higher pressure at depth, the speed of sound in seawater is generally higher than in fresh water. Step 3: Speed of Sound in Seawater at The speed of sound in seawater is a standard value that depends on these factors. At a temperature of , standard salinity (e.g., 35 parts per thousand), and atmospheric pressure (surface), the speed of sound is approximately . More precise empirical formulas (like those by Medwin or Mackenzie) exist for calculating it. A commonly cited value for "typical" surface seawater at is around to . Step 4: Comparing with the options
(1) 1531 m/s: This value is well within the expected range for seawater at and is a commonly referenced standard value.
(2) 1533 m/s: Also a very plausible value, very close to 1531 m/s.
(3) 1536 m/s: Slightly higher, but could be possible under specific salinity/pressure.
(4) 1498 m/s: This value is closer to the speed of sound in fresh water at around (or slightly warmer fresh water). Seawater speed is generally higher. Given that option (1) 1531 m/s is circled and is a widely accepted reference value for the speed of sound in seawater under conditions approximating and standard salinity at the surface, this is the most likely correct answer. Small variations exist based on exact salinity and pressure.

Concept: Waves can be broadly classified into two types based on their need for a medium to propagate: (A) Mechanical Waves: These waves require a material medium (solid, liquid, or gas) for their propagation. They travel by causing oscillations or vibrations of the particles of the medium. Energy is transferred through the medium. (B) Electromagnetic Waves: These waves do not require a material medium for their propagation. They can travel through a vacuum (like outer space). They consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. Step 1: Analyzing the nature of each wave type in the options
(1) Sound waves: Sound waves are mechanical waves. They need a medium (like air, water, or solids) to travel by causing compressions and rarefactions of the particles of the medium. Sound cannot travel through a vacuum.
(2) Earthquake waves (Seismic waves): Earthquake waves are mechanical waves that travel through the Earth's layers. They include P-waves (longitudinal) and S-waves (transverse), both requiring a material medium.
(3) Light waves: Light is an electromagnetic wave. Electromagnetic waves (which also include radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays) can travel through a vacuum. This is how light from the Sun reaches Earth.
(4) Water surface waves: These are mechanical waves that travel on the surface of water. They involve the motion of water particles and thus require water (a medium) to propagate. Step 2: Identifying the wave that does not require a medium From the analysis, Light waves are electromagnetic waves and do not require any kind of medium to propagate. They can travel through the vacuum of space.

Concept: The human ear can perceive sound waves only within a specific range of frequencies. This range is known as the audible range or hearing range. Step 1: Defining the Audible Range For a healthy young human, the generally accepted audible range of frequencies is from approximately 20 Hertz (Hz) to 20,000 Hertz (Hz). Frequencies below 20 Hz are called infrasound, and frequencies above 20,000 Hz are called ultrasound. Step 2: Understanding Frequency Units
Hz = Hertz (cycles per second)
KHz = Kilohertz = 1,000 Hz
GHz = Gigahertz = 1,000,000,000 Hz So, 20,000 Hz can be written as . Step 3: Identifying the upper limit of the audible range The lower limit is given as 20 Hz. The upper limit is 20,000 Hz, which is equivalent to 20 KHz. Step 4: Comparing with the options The question asks for the upper limit to complete the range "from 20 Hz to ___".
(1) 20 Hz: This would mean no range, which is incorrect.
(2) 20 KHz: This is equal to 20,000 Hz, which is the standard upper limit of human hearing.
(3) 20 GHz: This is , an extremely high frequency, far beyond human hearing (in the microwave range).
(4) 25 KHz: This is 25,000 Hz. While some individuals (especially young children) might hear slightly above 20 KHz, 20 KHz is the standard accepted upper limit for the general population. The most appropriate answer for the upper limit of the human audible range is 20 KHz.

Concept: Waves can be classified based on the direction of particle oscillation relative to the direction of wave propagation. Ultrasonic waves are sound waves with frequencies higher than the upper audible limit of human hearing (typically above 20 kHz). Step 1: Understanding different types of waves based on particle motion
Longitudinal Wave: In a longitudinal wave, the particles of the medium oscillate (vibrate) parallel to the direction in which the wave travels. These waves consist of compressions (regions of high density/pressure) and rarefactions (regions of low density/pressure). Sound waves (including audible sound, infrasound, and ultrasound) are examples of longitudinal waves.
Transverse Wave: In a transverse wave, the particles of the medium oscillate perpendicular to the direction in which the wave travels. These waves consist of crests and troughs. Light and other electromagnetic waves are examples of transverse waves. Waves on a string are also transverse. Step 2: Understanding other wave classifications given in options
Progressive Wave (or Traveling Wave): A wave that transfers energy from one point to another as it travels through a medium or vacuum. Both longitudinal and transverse waves can be progressive.
Stationary Wave (or Standing Wave): A wave that oscillates in time but whose peak amplitude profile does not move in space. It is formed by the superposition of two waves (often an incident wave and its reflection) traveling in opposite directions. Both longitudinal and transverse waves can form stationary waves. These classifications (Progressive/Stationary) describe the wave's behavior in terms of energy transfer and spatial movement, not the direction of particle oscillation. Step 3: Classifying Ultrasonic Waves Ultrasonic waves are essentially sound waves, just with frequencies too high for humans to hear. Sound waves are longitudinal waves. They propagate through a medium by causing compressions and rarefactions of the particles in that medium. Ultrasonic waves are also progressive waves as they travel and transfer energy. They can also form stationary waves under appropriate conditions. However, the question "Ultrasonic wave is a :" is primarily asking for its fundamental nature regarding particle motion. Step 4: Choosing the most appropriate classification The most fundamental classification based on the nature of particle oscillation is whether it's longitudinal or transverse. Since ultrasonic waves are a type of sound wave, they are longitudinal waves. Options (3) and (4) describe other aspects of wave behavior that can apply to both longitudinal and transverse waves. Option (1) is incorrect as sound waves are not transverse.