
A sound wave of frequency 245 Hz travels with the speed of $300\dfrac{m}{s}$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?
A. $Y = 0.03\sin \left[5.1x - \left(0.2 \times {10^3}t\right)\right]$
B. $Y = 0.06\sin \left[5.1x - \left(1.5 \times {10^3}t\right)\right]$
C. $Y = 0.06\sin \left[0.8x - \left(0.5 \times {10^3}t\right)\right]$
D. $Y = 0.03\sin \left[5.1x - \left(1.5 \times {10^3}t\right)\right]$
Answer
163.8k+ views
Hint: It is crucial to understand the meanings of travelling waves before moving on to the issue. A disturbance in a medium can be characterised as a wave if it propagates while transferring energy and momentum with no net motion of the medium. A travelling wave is one whose positions of maximum and minimum amplitude move through the medium.
Complete answer:
General expression for wave travelling along positive x axis is of the form
$Y = A\sin (kx - \omega t)$
Given that,
$f = 245Hz$
$v = 300\dfrac{m}{s}$
Here we have $A = \dfrac{6}{2} = 3cm$
$\omega = 2\pi f$
$ \Rightarrow \omega = 2\pi \times 245 = 1.54 \times {10^3}\dfrac{{rad}}{{\sec }}$
$k = \dfrac{\omega }{v} = \dfrac{{1.54 \times {{10}^3}}}{{300}}$
$k = 5.1{m^{ - 1}}$
So mathematical expression of travelling wave will be given by
$Y = 0.03\sin \left[5.1x - \left(1.5 \times {10^3}t\right)\right]$
Therefore, the correct answer is option (D).
Additional information:
1. The medium must, nevertheless, possess elastic characteristics.
2. The maximum distance of the disturbance from the wave's midpoint to the top of the crest or the bottom of the trough is known as the amplitude.
3. A wavelength is the maximum separation between two adjacent troughs.
4. The time now truly refers to the duration of one vibration.
5. The number of vibrations a wave makes in one second is its frequency.
6. Both frequency and duration exhibit an inverse relationship. The connection is shown below,
$T = \dfrac{1}{f}$
The speed of a wave is given by,
$v = \lambda f$
Where $\lambda$ is the wavelength.
Note: Students might mistake in the question to write amplitude 6 cm but it’s not correct. Half of the amplitude complete length is provided to us. Always keep that in mind. A crucial second-order linear partial differential equation for the description of waves is the wave equation
Complete answer:
General expression for wave travelling along positive x axis is of the form
$Y = A\sin (kx - \omega t)$
Given that,
$f = 245Hz$
$v = 300\dfrac{m}{s}$
Here we have $A = \dfrac{6}{2} = 3cm$
$\omega = 2\pi f$
$ \Rightarrow \omega = 2\pi \times 245 = 1.54 \times {10^3}\dfrac{{rad}}{{\sec }}$
$k = \dfrac{\omega }{v} = \dfrac{{1.54 \times {{10}^3}}}{{300}}$
$k = 5.1{m^{ - 1}}$
So mathematical expression of travelling wave will be given by
$Y = 0.03\sin \left[5.1x - \left(1.5 \times {10^3}t\right)\right]$
Therefore, the correct answer is option (D).
Additional information:
1. The medium must, nevertheless, possess elastic characteristics.
2. The maximum distance of the disturbance from the wave's midpoint to the top of the crest or the bottom of the trough is known as the amplitude.
3. A wavelength is the maximum separation between two adjacent troughs.
4. The time now truly refers to the duration of one vibration.
5. The number of vibrations a wave makes in one second is its frequency.
6. Both frequency and duration exhibit an inverse relationship. The connection is shown below,
$T = \dfrac{1}{f}$
The speed of a wave is given by,
$v = \lambda f$
Where $\lambda$ is the wavelength.
Note: Students might mistake in the question to write amplitude 6 cm but it’s not correct. Half of the amplitude complete length is provided to us. Always keep that in mind. A crucial second-order linear partial differential equation for the description of waves is the wave equation
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
