Two waves are represented by: y1=4 sin404 πt and y2=3 sin400 πt. Then (a) beat frequency is 4 H

Name: Problem 62, Chapter 12: Objective Physics for NEET
Uploaded: 2021-09-05T16:11:43-08:00
Duration: 1 min 38 s
Channel: Ajay Singhal

step 1 Hello students in this question we have given the two waves that is y1 equals to 4 sign of 404 p

Question

Two waves are represented by: $y_{1}=4 \sin 404 \pi t$ and $y_{2}=3 \sin 400 \pi \mathrm{t}$. Then (a) beat frequency is $4 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $49: 1$ (b) beat frequency is $2 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $49: 1$ (c) beat frequency is $2 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is I : 49 (d) beat frequency is $4 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $1: 49$

   Two waves are represented by: $y_{1}=4 \sin 404 \pi t$ and $y_{2}=3 \sin 400 \pi \mathrm{t}$. Then
(a) beat frequency is $4 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $49: 1$
(b) beat frequency is $2 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $49: 1$
(c) beat frequency is $2 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is I : 49
(d) beat frequency is $4 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $1: 49$

Objective Physics for NEET

Abhay Kumar 1st Edition

Chapter 12, Problem 62

Instant Answer

Solved by Expert Ajay Singhal

09/05/2021

Step 1

The angular frequency $\omega$ is related to the frequency $f$ by the equation $\omega = 2\pi f$. So, we can find the frequencies $f_1$ and $f_2$ of the two waves by dividing their angular frequencies by $2\pi$. For the first wave, we have $\omega_1 = 404\pi$, so Show more…

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Two waves are represented by: $y_{1}=4 \sin 404 \pi t$ and $y_{2}=3 \sin 400 \pi \mathrm{t}$. Then (a) beat frequency is $4 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $49: 1$ (b) beat frequency is $2 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $49: 1$ (c) beat frequency is $2 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is I : 49 (d) beat frequency is $4 \mathrm{~Hz}$ and the ratio of maximum to minimum intensity is $1: 49$

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Key Concepts

Amplitude and Intensity Relationship

In wave phenomena, the intensity of a wave is proportional to the square of its amplitude. This relationship is used to determine the variations in energy output during interference, such as finding the ratio between maximum and minimum intensities when waves combine.

Superposition Principle

This principle states that when two or more waves meet, their displacements add algebraically to produce a new wave pattern. It underlies the concept of interference, where the combined effect can lead to enhancements (constructive interference) or reductions (destructive interference) in amplitude.

Beat Frequency

Beat frequency is the rate at which the amplitude of the resultant wave oscillates due to the interference of two waves of slightly different frequencies. It is calculated as the absolute difference between the two frequencies, resulting in a perceptible pulsation when the waves merge.

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