
Two tones of frequencies \[{n_1}\] and \[{n_2}\] are sounded together. The beats can be heard distinctly when
A. \[10 < ({n_1} - {n_2}) < 20\]
B. \[5 < ({n_1} - {n_2}) > 20\]
C. \[5 < ({n_1} - {n_2}) < 20\]
D. \[0 < ({n_1} - {n_2}) < 10\]
Answer
164.1k+ views
Hint: As we know that beat is produced when two waves of nearby frequencies superimpose when both travel in the same path. The beat frequency is defined as the number of beats produced per second.
Formula used
The formula for beat frequency is given as,
\[n = {n_1} - {n_2}\]
Where \[{n_1}\] and \[{n_2}\] is the frequency of two waves.
Complete step by step solution:
Given two tones of frequencies sounded together are \[{n_1}\]and \[{n_2}\]. As we know that the efficiency of human ears to listen to a sound must be at least one beat per 0.1 second otherwise if it is less than 0.1 second then we are not able to listen to that sound. So to listen to the 1 beat, the time must be 0.1 sec.
i.e., 1 beat = 0.1 sec
Also, we can write 10 beats = 1 sec. It shows in 1 sec there are a total 10 beats. This is the maximum efficiency.
If time decreases from 0.1 sec (like 0.01 sec), the efficiency of the human ear will also decrease. As the number of beats per second is given by the difference of frequencies. If \[{n_1}\]and \[{n_2}\] are two tones of frequencies sounded together. So (\[{n_1} - {n_2}\]) produces the beat and has to be less than 10 or greater than 0. Therefore, the beats can be heard distinctly when \[0 < ({n_1} - {n_2}) < 10\].
Hence option D is the correct answer.
Note: The formula for beat frequency is the difference in frequency of the two superimposed waves. Due to this there is a cause in a periodic variation of intensity of the resultant wave. The phenomenon of the beats can take place in both longitudinal waves as well as transverse waves.
Formula used
The formula for beat frequency is given as,
\[n = {n_1} - {n_2}\]
Where \[{n_1}\] and \[{n_2}\] is the frequency of two waves.
Complete step by step solution:
Given two tones of frequencies sounded together are \[{n_1}\]and \[{n_2}\]. As we know that the efficiency of human ears to listen to a sound must be at least one beat per 0.1 second otherwise if it is less than 0.1 second then we are not able to listen to that sound. So to listen to the 1 beat, the time must be 0.1 sec.
i.e., 1 beat = 0.1 sec
Also, we can write 10 beats = 1 sec. It shows in 1 sec there are a total 10 beats. This is the maximum efficiency.
If time decreases from 0.1 sec (like 0.01 sec), the efficiency of the human ear will also decrease. As the number of beats per second is given by the difference of frequencies. If \[{n_1}\]and \[{n_2}\] are two tones of frequencies sounded together. So (\[{n_1} - {n_2}\]) produces the beat and has to be less than 10 or greater than 0. Therefore, the beats can be heard distinctly when \[0 < ({n_1} - {n_2}) < 10\].
Hence option D is the correct answer.
Note: The formula for beat frequency is the difference in frequency of the two superimposed waves. Due to this there is a cause in a periodic variation of intensity of the resultant wave. The phenomenon of the beats can take place in both longitudinal waves as well as transverse waves.
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
