Arjuna JEE 2.0 Physics DPP 1

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Questions and Answers

What is the speed of the wave motion in the given equation?

600 m/s

300 m/s

450 m/s

200 m/s (correct)

What is the angular frequency of the progressive wave represented by the equation y = 10 sin 2π (x/8 + t/4)?

2π

8π

4π (correct)

What is the correct relationship between frequency and wavelength for the wave function given?

Frequency is 2 Hz and wavelength is 4 metre

Frequency is 8 Hz and wavelength is 2 metre

Frequency is 4 Hz and wavelength is 16 metre

Frequency is 4 Hz and wavelength is 8 metre (correct)

What is the amplitude of the wave given by the equation y = 10 sin 2π (x/8 + t/4)?

10 metre Signup and view all the answers

What is the propagation constant for the wave function y = 10 sin 2π (x/8 + t/4)?

π Signup and view all the answers

How does the frequency of the wave relate to its period?

Frequency is the inverse of the period Signup and view all the answers

In the equation for the wave y = 10 sin 2π (x/8 + t/4), how is the wavelength determined?

From the coefficient of x in the argument of the sine function Signup and view all the answers

What would be the effect on the wave if the amplitude were increased to 15 metre?

The wave would be taller but maintain the same frequency Signup and view all the answers

What is the speed of the wave described by the equation $y = 4 \sin[\frac{\pi}{2}(8t - \frac{x}{4})]$?

32 cm/s along −x direction Signup and view all the answers

Which statement correctly describes a characteristic of the pulse represented by the equation $y = 4 + (x + 4t)$?

The speed of pulse is 4 m/s Signup and view all the answers

For the wave equation $y = 5 \cos(300t - 1.5x + \frac{\pi}{4})$, what is the wavelength?

$\frac{2\pi}{1.5}$ m Signup and view all the answers

Which equation represents a harmonic wave condition?

$\frac{d^2y}{dt^2} = v \frac{d^2y}{dx^2}$ Signup and view all the answers

How many wavelengths are there in a distance of XY if the correct wavelength is established?

180 Signup and view all the answers

What condition must be satisfied for the given wave to be classified as a harmonic wave?

$\frac{d^2y}{dx^2} = \frac{1}{v^2} \frac{d^2y}{dt^2}$ Signup and view all the answers

What is the correct relationship between frequency, wavelength, and velocity of propagation of a wave?

n = v/λ Signup and view all the answers

In the equation $y = 4 + (x + 4t)$, what is represented by the term '4'?

The baseline or equilibrium position Signup and view all the answers

From the wave equation $y = 5 \cos(300t - 1.5x + \frac{\pi}{4})$, what is the approximate frequency?

300 Hz Signup and view all the answers

Which type of wave involves particle motion perpendicular to the direction of wave travel?

Transverse waves Signup and view all the answers

If the speed of the wave is 32 cm/s, what is the relationship between wave speed, wavelength, and frequency?

$v = f \lambda$ with $\lambda$ = 2 m Signup and view all the answers

What is the expression that relates phase difference to path difference for waves?

Δϕ = 2πΔx/λ Signup and view all the answers

Given the wave equations y1 = A cos ωt and y2 = A sin ωt, how does the phase of the first wave relate to the second?

leads the second by π/2 Signup and view all the answers

If a wave travels a distance of 600 m in 4 seconds, what is its velocity?

150 m/s Signup and view all the answers

What is the relationship between phase difference (Δϕ) and wavelength (λ) in the context of wave propagation?

Δϕ = 2πΔx/λ Signup and view all the answers

In wave mechanics, which of the following correctly defines longitudinal waves?

Particles vibrate parallel to the direction of wave motion. Signup and view all the answers

If the wavelength of a wave is doubled, how does this affect its frequency, assuming velocity remains constant?

Frequency halves. Signup and view all the answers

What type of wave is characterized by alternating regions of compression and rarefaction?

Longitudinal waves Signup and view all the answers

What defines stationary waves?

They are formed by the interference of two waves traveling in opposite directions. Signup and view all the answers

Study Notes

Waves and Key Concepts in Physics

Frequency, Wavelength, and Velocity Relation: The relationship among frequency (n), wavelength (λ), and velocity (v) of a wave is given by n = v/λ.
Phase Difference and Path Difference: The relation between phase difference (Δϕ) and path difference (Δx) is defined as Δϕ = (2π/λ)Δx.
Types of Waves: Waves where particles of the medium vibrate perpendicular to the direction of wave motion are called transverse waves.
Wave Equations: For two waves represented by equations y1 = A cos(ωt) and y2 = A sin(ωt), it can be noted that y1 leads y2 by π/2 (90 degrees).
Calculating Wavelengths: For a wave with a frequency of 500 Hz traveling 600 m in 4 seconds, the number of wavelengths can be calculated. The speed of the wave is 150 m/s, indicating 2000 wavelengths in the distance.
Progressive Wave Equation: The equation y = 4 sin(π/2 (8t - x)) represents a progressive wave. Velocity can be determined from this equation as v = 32 cm/s in the positive x direction.
Displacement of a Wave: Given the equation y = 5 cos(300t - 1.5x + π/4), where x is in metres and t in seconds, the speed of the wave is calculated to be 200 m/s.
Properties of Progressive Waves: The progressive wave represented by y = 10 sin(2π( (x/8) + (t/4))) has an amplitude of 10 meters, a frequency of 1/4 Hz, and a wavelength of 8 meters.
Angular Frequency and Propagation Constant: In the standard form of wave equations, angular frequency (ω) is related to the wave's frequency, and the propagation constant (k) relates to the wave's wavelength.

Sample Questions and Answers

Wave Velocity Calculation: To find wave velocity, use v = frequency × wavelength.
Understanding Wave Types: Transverse waves differ from longitudinal waves where particles move parallel to wave motion.
Wavelength Determination: The total number of wavelengths present in a specific distance can be computed using the formula relating frequency, speed, and wavelength.
Translating Wave Functions: The derived parameters from wave functions satisfy the wave equation criteria essential for harmonic waves, reinforcing the relationship between displacement, velocity, and wave propagation.
Wave Amplitude and Shape: The amplitude influences the maximum displacement in wave functions, indicating the energy transmitted through the wave medium.

Exam Preparation Tips

Familiarize with wave properties and equations.
Practice calculating wave velocity, frequency, and wavelengths.
Review different types of waves and their characteristics.
Master the conceptual understanding of phase difference and path difference relationships.
Solve previous year questions to solidify knowledge and get accustomed to the exam format.

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Description

Test your knowledge on waves with this quiz from Arjuna JEE 2.0 (2024). Covering important concepts and relations, this quiz is essential for JEE aspirants. Challenge yourself with multiple questions designed to strengthen your understanding of wave physics.

Arjuna JEE 2.0 Physics DPP 1 - Waves