Test: Waves - NEET MCQ

y₁ = A₁ sin wt

y₂ = A₂ cos (wt + f)

Now, y₂ can be rewritten as A₂ sin (wt + f + π/2)

So, the phase difference is f + π/2

Path Difference = (λ/2π)(f + π/2)

Hence, the correct option is b.

Two sources are said to be coherent if there always exists a constant phase difference between the waves emitted by these sources. But when the sources are coherent, then the resultant intensity of light at a point will remain constant and so interference fringes will remain stationary.

The necessary condition for phenomenon of interference to occur are:
1. There should be two coherent sources.
2. The frequency and amplitude of both the waves should be same.
3. The propagation of waves should be simultaneously and in same direction.
These are the conditions, no explanation.

Calculation:

For Case 1 :

For Case 2 :

From (i) and (ii)

288 f_app = 240 × 240

f_app = 200 Hz

Let the distance to the epicenter of the earthquake be d km. The time taken by the P waves to travel this distance is t_P​, and the time taken by the S waves to travel this distance is t_S​.

We know that:

t_S ​− t_P​ = 4minutes = 240seconds.

The relationship between speed, distance, and time is:

t = d/v​,

where v is the velocity and t is the time.

For the P waves:

t_P ​= d/8.0​.

For the S waves:

t_S ​= d​/4.5

From the time difference:

t_S − t_P = 240

Substitute the expressions for t_S​ and t_P​:

Find a common denominator and solve:

Simplify:

Thus, the distance to the epicenter is approximately 2500 km.

Let the distance to the epicenter of the earthquake be d km. The time taken by the P waves to travel this distance is t_P​, and the time taken by the S waves to travel this distance is t_S​.

We know that:

t_S ​− t_P​ = 4minutes = 240seconds.

The relationship between speed, distance, and time is:

t = d/v​,

where vvv is the velocity and ttt is the time.

For the P waves:

t_P ​= d/8.0​.

For the S waves:

t_S ​= d​/4.5

From the time difference:

t_S − t_P = 240

Substitute the expressions for t_S​ and t_P​:

Find a common denominator and solve:

Simplify:

Thus, the distance to the epicenter is approximately 2500 km.

The observer will hear two sounds, one directly from the source and the other reflected image of sound. Hence, the number of beats heard per second is

When the source approaches the observer Apparent frequency 

(Neglecting higher powers because v_s≪v)

When the source recedes the observed apparent frequency 

Given 

= 3 m/sec

The correct answer is 5 seconds

•  To calculate the time it takes for a sound wave to travel a distance, we can use the formula:
  • ​Distance/ Speed of Sound
• We are given:
  • Distance = 1.5 km = 1500 meters
• Frequency of the sound wave = 5 kHz = 5000 Hz
  • Wavelength = 6 cm = 0.06 meters
• First, we need to calculate the speed of sound using the formula:
  • Speed of sound = Frequency × Wavelength
• Substituting the given values:
  • ​Speed of sound = 5000Hz × 0.06m=300m/s
• Now, we can calculate the time taken for the sound wave to travel 1500 meters:
  • ​Time = 1500m/300m/s = 5 Seconds

• Frequency: The number of waves that pass a fixed point in unit time.
  • The unit of frequency is Hertz (Hz).
• Infrasonic sounds have a frequency of less than 20 Hz and these are generally produced by sources of a bigger size such as earthquakes, volcanic eruptions, etc.
• Sound waves with frequencies below the audible range are called infrasonic.
  • Audible sounds have a frequency of 20-20000 Hz since these are sensitive to the human ears
• And if the frequency is greater or less than audible frequency, the human ear won't be able to sense it
• Ultrasonic sounds have a frequency greater than 20000 Hz and certain creatures such as dogs, cats, bats can hear this kind of sound.

• Human ears are capable of hearing between 20 Hz to 20000 Hz.
• Bats are capable of here sound above 20 kHz (ultrasound).
• Elephants are capable of here sound below 20 Hz (infrasound).

Frequency can be divided into three categories based on their frequency range:

• Audible sound waves: The frequency range of this wave is 20Hz - 20000Hz. Humans can easily detect these types of waves.
  • Example: Sound produced by Vocal cords.
• Infrasonic waves: The frequency range of these types of waves is below 20Hz. Humans cannot detect it.
  • Example: Elephants, Sound produced by Earthquake, Volcanic eruption and ocean waves, Weather, Lee waves, Avalanche, Waterfalls, Meteors, Lightening, etc.
• Ultrasonic waves or Ultrasound waves: The sound frequency above 20,000Hz is known as ultrasonic waves. Humans cannot detect it too.
  • Examples: dog whistle, Dolphins, Bats, Porpoises, and Rats are examples of an Ultrasound wave.

So,

• From the above discussion, we can say that the infrasonic sound is produced by elephants. 
• Elephants can communicate by using very low-frequency sounds, with pitches below the range of human hearing. By this hypothesis, elephant infrasounds.
• So option 3 is correct.

CONCEPT:

• Wavelength (λ): The space or length between two successive crests or troughs of a wave is called the wavelength.

​​

• Frequency (f): It is the number of occurrences of a repeating event per unit of time. Its SI unit is Hertz (Hz).
• Velocity (v): Velocity is defined as the rate of change of displacement of a body with respect to time. The SI unit is meter per second (ms-1).

​The speed can be calculated using the formula: 

speed (v) = wavelength (λ) x frequency (f).

So,

Given that: 

Wavelength (λ) = 2 m

Frequency (f) = 200 Hz

Speed (v) = f × λ 

 ⇒ v = 200 x 2

 ⇒ v = 400 m/s. Hence option 1 is correct.

The correct answer is the Transverse wave.

• Light is a Transverse wave.

Key Points

• Light is a form of energy that is propagated as electromagnetic waves.
• Electromagnetic waves are transverse, hence light is a transverse wave.
• The wave nature of light explains rectilinear propagation, reflection, refraction, interference, diffraction, and polarization of light.
• In quantum theory, light is regarded as a packet or bundle of energy called the photon.
• Light behaves as wave and particle both. Thus light has dual nature.
• Speed of light is maximum in vacuum and air (3 × 10⁸ m/s).

CONCEPT:

•  Sound in air: In a gas like air, the particles are generally far apart so they travel further before they bump into one another. There is not much resistance to movement so it doesn’t take much to start a wave, but it won’t travel as fast.
• Sound in water: In water, the particles are much closer together, and they can quickly transmit vibrational energy from one particle to the next. This means that the sound wave travels over four times faster than it would in air, but it takes a lot of energy to start the vibration.

• Sound in solids: In a solid, the particles are even closer together and linked by chemical bonds so the wave travels even faster than it does in either liquid or air, but you need quite a lot of energy to start the wave at the beginning
• Sound waves travel faster in denser substances because neighboring particles will more easily bump into one another. Water is denser than air, so the speed of sound is more in water than in air. So option c is correct.

CONCEPT:

• Wave: The disturbance that transfers energy from one place to another is called a wave.

There are mainly two types of waves:

• Electromagnetic waves: The wave which is generated due to vibration between electric field and magnetic field and it does not need any medium to travel is called an electromagnetic wave. It can travel through a vacuum.
  • Light is a form of energy which is an example of electromagnetic waves.
  • Electromagnetic waves are transverse in nature because they propagate by varying their electric and magnetic fields so that both the fields propagate perpendicular to each other.
• Mechanical waves: The oscillation of matter which is responsible for the transfer of energy through a medium is called a mechanical wave.
  • It can’t travel through a vacuum.
  • Examples: Sound wave, wave in a string, water wave.

Therefore,

• The vacuum is the medium from where the sound wave cannot pass. A vacuum is basically an area without any air.
• Since the sound wave is a mechanical wave that's why it cannot travel through a medium where there is no matter of vibrations to works in, i.e, it can't travel through a vacuum. So option 2 is correct.
• The sound wave can travel through solids, liquid and gas medium.

The correct answer is Magnetic waves. 

• MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body.
• MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from CT or CAT scans and PET scans.

Key Points

• MRI can be also known or called Magnetic Resonance imaging.
• In MRI the body is placed in a high strength magnetic field.
• This field is generated by a superconducting magnetic coil which is immersed in liquid helium.
• This field causes the alignment of the spins of the protons in the body of the patient.
• Pulses of radio waves are then used to excite the nuclei causing the alignment of the spins to undergo decoherence.
• When the spins realign, they release a radio signal which is picked up by antennae placed close to the body.
• from this signal and by modulating the radio wave pulses different types of MR images are reconstructed.
• This is the basis of MR imaging.

Concept:

• Echo: An echo is a sound caused by the reflection of sound waves from a surface back to the listener.
• It reflects sound, arriving at the listener sometime after the direct sound.

• The velocity formula for the echo is given as, v = 2dt where d = distance between the source and reflectors, t = time taken to reflect back the echo.

Calculation:

Given,

Time, t = 1 s

The velocity of the sound in air, v = 340 ms^-1

Let's consider d is the distance between the man and the mountain.

The sound wave travels two times between the mountain and the man. 

So, v = 2dt

2d = vt

d = vt/2

d = 340 × 1 / 2 = 170 m

Hence, the distance between the man and the mountain is 170m.

CONCEPT:

• Wavelength (λ): The space or length between two successive crests or troughs of a wave is called the wavelength.

​​

• Frequency (f): It is the number of occurrences of a repeating event per unit of time. Its SI unit is Hertz (Hz).
• Velocity (v): Velocity is defined as the rate of change of displacement of a body with respect to time. The SI unit is meter per second (ms-1).

​The speed can be calculated using the formula: 

speed (v) = wavelength (λ) x frequency (f).

Therefore,

Given that: 

Wavelength (λ) = 0.5 m

Frequency (f) = 640 Hz

Speed (v) = f × λ 

 ⇒ v = 0.5 x 640

 ⇒ v = 320 m/s. Hence option D is correct.