Waves MCQs for NEET — Physics Questions with Answers

(d)  $y=5\sin \left(\mathrm{\pi t}+4\mathrm{\pi }\right),$comparing it with standard equation

 $y=a\sin \left(\omega t+\varphi \right)=a\sin \left(\frac{2\mathrm{\pi t}}{T}+\varphi \right)$

$$\begin{gathered} a=5m and \frac{2\mathrm{\pi t}}{T}=\mathrm{\pi t} \\ \Rightarrow \mathrm{T}=2 \sec \end{gathered}$$

(b) $A=\frac{c}{a+b-c}$when ,b=0 , a=c 

Amplitude     $A\to \infty$. This corresponds to resonance.

(b)

 $$\begin{gathered} y=4 {\cos }^2\left(\frac{t}{2}\right)\sin 1000t \\ \Rightarrow y=2\left(1+\cos t\right) \sin \left(1000t\right) \left(As 1+\cos t=1+2{\cos }^2\left(\frac{t}{2}\right)-1=2{\cos }^2\left(\frac{t}{2}\right)\right) \\ \Rightarrow y=2 \sin 1000t+2 \sin 1000t \cos t \\ \Rightarrow y=2 \sin 1000t+\sin \left(1000t-t\right)+\sin (1000t+t) \left[2\sin A\cos B=\sin \left(A+B\right)+\sin \left(A-B\right)\right] \\ \Rightarrow y= 2 \sin 1000t + \sin 999t+ \sin 1001t \\ \mathrm{It} \mathrm{is} \mathrm{a} \mathrm{sum} \mathrm{of} \mathrm{three} \mathrm{S}.\mathrm{H}.\mathrm{M}. \end{gathered}$$

$$\begin{gathered} \mathrm{y} = \mathrm{a} \sin \left(\mathrm{\omega t} - \mathrm{kx}\right) \\ \mathrm{speed} \mathrm{of} \mathrm{wave} = \frac{\mathrm{\omega }}{\mathrm{k}} \\ = \frac{314}{3.14} = 100 \mathrm{m}/\mathrm{s} \end{gathered}$$

$y=A \log x +B\log x is not a wave.$

2$\pi$

$$\begin{gathered} \mathrm{v} = \sqrt{\frac{{\mathrm{E}}_{}}{\mathrm{\rho }}}\left\{\mathrm{Laplace} \mathrm{formula}\right\} \\ \mathrm{v} \propto \sqrt{{\mathrm{E}}_{\mathrm{a}}} \end{gathered}$$

When a wave undergoes a reflection at a denser medium then it's crest reflected as a trough and vice versa.

When a source of sound moves away from a stationary observer, the frequency heard by the observer decreases due to the Doppler effect. The observed frequency is given by f' = f * (v - v_s) / (v + v_s), where f is the source frequency, v is the speed of sound, and v_s is the speed of the source. As the source moves away with the speed of sound, the observed frequency is halved.

4.  In liquids, solids, and gases