34. The displacement of a progressive wave is represented by y = A sin (ωt - kx) where x is distance and t is time. The dimensions of ω/k are the same as those of:
(A) velocity
(B) wave number
(C) wavelength
(D) frequency

35. The incorrect statement is:
(A) Dimensional analysis cannot be used to check the correctness of equations involving trigonometric functions.
(B) Dimensional analysis can be used to deduce the equation which are only dimensionally correct.
(C) Dimensional analysis can be used to determine the constants of proportionality.
(D) Dimensional analysis can be used to deduce equations which are of product type.

For question 34, we are given the displacement equation of a progressive wave: y = A sin ( ω t − k x ) where x is distance and t is time. We need to find the dimension of k ω ​ and compare it to the given options.
Step-by-step analysis:

Understanding ω and k :


ω is the angular frequency and has the dimension of [ T − 1 ] since it is related to the frequency by ω = 2 π f .

k is the wave number and has the dimension of [ L − 1 ] since it is defined as k = λ 2 π ​ where λ is the wavelength.



Find dimensions of k ω ​ :


k ω ​ = [ L − 1 ] [ T − 1 ] ​ = [ L ] [ T − 1 ] .


Compare with the options:


(A) Velocity has the dimension [ L ] [ T − 1 ] .

(B) Wave number has the dimension [ L − 1 ] .

(C) Wavelength has the dimension [ L ] .

(D) Frequency has the dimension [ T − 1 ] .


Based on this analysis, k ω ​ has the same dimension as velocity, [ L ] [ T − 1 ] .
Chosen Option: (A) Velocity
For question 35, let's verify each statement using our understanding of dimensional analysis:

(A) Dimensional analysis cannot be used to check the correctness of equations involving trigonometric functions.


This statement is true. Trigonometric functions are dimensionless, so checking dimensions in a function involving them does not validate the equation.


(B) Dimensional analysis can be used to deduce the equation which are only dimensionally correct.


This statement is true. Dimensional analysis helps verify if an equation might be correct dimensionally, but it cannot ensure physical correctness.


(C) Dimensional analysis can be used to determine the constants of proportionality.


This statement is false. Dimensional analysis cannot be used to find numerical values of dimensionless constants.


(D) Dimensional analysis can be used to deduce equations which are of product type.


This statement is true. Dimensional analysis can suggest forms of equations that are products of variables with appropriate dimensions.

Chosen Option: (C) Dimensional analysis can be used to determine the constants of proportionality, which is incorrect.

Answered by EmmaGraceJohnson | 2025-07-06