Waves Test - 38...

Two simple harmonic motions are given by:
$$ { x }_{ 1 }=a\sin { \omega t } +a\cos { \omega t } $$
$${ x }_{ 2 }=a\sin { \omega t } +\cfrac { a }{ \sqrt { 3 }  } \cos { \omega t } $$
The ratio of the amplitudes of first and second motion and the phase difference between them are respectively:

What is the phase difference between two simple harmonic motions represented by $$x_{1} = A\sin \left (\omega t + \dfrac {\pi}{6}\right )$$ and $$x_{2} = A \cos (\omega t)$$?

A pulse of a wave travelling on a string towards the fixed rigid end as shown in the figure above. The pulse is:

With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the direction of propagation are

Find out the amplitude of the travelling wave given in above figure?

The frequency of a sound wave is 200 Hz and its wavelength is 150 cm.  What is the distance travelled by the sound wave in the time taken to produce 150 waves?

Find out the change in wavelength of a $$700 Hz$$ acoustic wave as it enters brass from warm air? Given Speed of Sound in warm air is  $$350 {m}/{s}$$ and through brass is $$3,500 {m}/{s}$$.

Two travelling waves of equal frequency, with amplitude $$4 cm$$ and $$6 cm$$ respectively, superimpose in a single medium. Find out the range of the amplitude, $$A$$, of the resultant wave?

Two simple harmonic motions are given by
$$x_1 = a \sin \omega t + a \cos \omega t$$ and
$$x_2 = a \sin \omega t + \dfrac{a}{\sqrt{3}}\cos \omega t$$
The ratio of the amplitudes of first and second motion and the phase difference between them are respectively

The S.I unit of wavelength is ______________