Statement-1`:` Two longitudinal waves given by equation `y_(1)(x,t)=2asin(omegat-kx)`
and `y_(2)(x,t)=a sin (2 omegat-2kx)`
will have equal intensity.
Statement-2 `:` Intensity of waves of given frequency ini same medium is proportioal to square of amplitude only.

Options

A. Statement-1 is false, statement -2 is true.
B. Statement-1 is true, statement-2 is false.
C. Statement-1 is true, statement-2 is true, statement-2 is the correct explanation of statement-1.
D. Statement-1 is true, statement-2 is true, statement-2 is not correct explanation of statement-1.

Answer

b

Explanation

We know that intensity `(I)` of a wave.
(i) is directly proportinoal to square of amplitude `(A)`
(ii) is directlly proportional to square of angular frequency `(omega)`
i.e., `Iprop A^(2)omega^(2)`
For first wave, `I_(1)prop(2a)^(2)xxomega^(2)`
or `I_(1)=k4a^(2)omega^(2)`
For second wave, `I_(2) prop(a)^(2)xx(2omega)^(2)`
or` I_(2)k4a^(2)omega^(2)`
i.e., Intensity depends upon frequency also. Thus statement 1 is true but statment 2 is false.