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QNEET-2024-Ph-160: NEET 2024 Physics - Class 11 NEET-2024-Ph-160 Solution: The displacement of a travelling wave \(y = C {2 }{ }(at - x)\) …
The displacement of a travelling wave where t is time x is distance and is the wavelength all in S.I. units. Then the frequency of the wave is
Multiple Choice Options
- A a 2 �_ _
- B _ 2 �a _
- C a _ _
- D _ a _
Step-by-Step Verified Solution
To find the frequency of the wave, we need to start by analyzing the given displacement equation of the wave:
y = C sin _ ( 2 � _ ( a t _ x ) )
Where:
y is the displacement of the wave
C is the amplitude
2 � _ is the wave number (denoting how many wavelengths fit into a unit length)
_ is the wavelength
a is some constant (likely representing the speed of the wave)
t is time
x is the distance
By comparing with the standard form of a travelling wave, we have:
y = C sin _ ( k ( a t _ x ) )
Where k is the wave number:
k = 2 � _
From the standard wave equation, the argument of the sine function is usually written as:
k ( a t _ x )
This implies that k a in the wave equation represents the angular frequency _ of the wave:
_ = k a
Substituting k = 2 � _ into _ :
_ = ( 2 � _ ) a = 2 � a _
Angular frequency _ is related to the frequency f by:
_ = 2 � f
So:
2 � f = 2 � a _
Solving for the frequency f :
f = a _
Therefore, the correct answer is:
Option D: a _