
When two sound waves travel in the same direction in a medium the displacements of a particle located at 'x' at the time 't' is given by
\[{y_1} = 0.05\cos (0.50\pi x - 100\pi t)\]
\[{y_2} = 0.05\cos (0.46\pi x - 92\pi t)\] where \[{y_1},{y_2}\]and x are the meters and t in seconds. Find the speed of sound in the medium.
A. \[92m/s\]
B. \[200m/s\]
C. \[100m/s\]
D. \[332m/s\]
Answer
163.5k+ views
Hint: Speed of a wave is the distance at which a wave travels in a given amount of time, that is the number of meters it travels per second. It is related to the angular wave number and the frequency of a wave. The angular frequency is a vector quantity.
Formula used:
To find the speed of the wave the formula is,
\[V = \dfrac{\omega }{k}\]
Where,
\[\omega \] is angular frequency of the wave
k is angular wave number
Complete answer:
Consider a wave which is travelling in the same direction in a medium that is located at point x at a given time t. We need to find the speed of the sound at which it travels in a medium.
In order to find the speed of the wave we have,
\[V = \dfrac{\omega }{k}\]
By data, we have angular frequency as \[100\pi \] and an angular wave number is \[0.50\pi \]
Substitute the value in the above equation, we get,
\[V = \dfrac{{100\pi }}{{0.50\pi }}\]
\[V = 200m/s\]
Therefore, the speed of sound in the medium is \[200m/s\]
Hence, Option B is the correct answer
Note: Here, while solving this problem, it is important to know the formula for the speed of the wave. Don’t get confused with the formula, this is the formula to find the speed of the wave in terms of angular frequency.
Formula used:
To find the speed of the wave the formula is,
\[V = \dfrac{\omega }{k}\]
Where,
\[\omega \] is angular frequency of the wave
k is angular wave number
Complete answer:
Consider a wave which is travelling in the same direction in a medium that is located at point x at a given time t. We need to find the speed of the sound at which it travels in a medium.
In order to find the speed of the wave we have,
\[V = \dfrac{\omega }{k}\]
By data, we have angular frequency as \[100\pi \] and an angular wave number is \[0.50\pi \]
Substitute the value in the above equation, we get,
\[V = \dfrac{{100\pi }}{{0.50\pi }}\]
\[V = 200m/s\]
Therefore, the speed of sound in the medium is \[200m/s\]
Hence, Option B is the correct answer
Note: Here, while solving this problem, it is important to know the formula for the speed of the wave. Don’t get confused with the formula, this is the formula to find the speed of the wave in terms of angular frequency.
Recently Updated Pages
Fluid Pressure - Important Concepts and Tips for JEE

JEE Main 2023 (February 1st Shift 2) Physics Question Paper with Answer Key

Impulse Momentum Theorem Important Concepts and Tips for JEE

Graphical Methods of Vector Addition - Important Concepts for JEE

JEE Main 2022 (July 29th Shift 1) Chemistry Question Paper with Answer Key

JEE Main 2023 (February 1st Shift 1) Physics Question Paper with Answer Key

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

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

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

Charging and Discharging of Capacitor

Other Pages
NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

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

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

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

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

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