2 Marks Questions

Question 12 Marks

At what temperatures ($in ^oC$) will the speed of sound in air be 3 times its value at $O^oC$?

Answer

We know that speed of sound in air $\text{v}=\sqrt{\frac{\gamma\text{RT}}{\text{M}}}\Rightarrow\text{v}\propto\sqrt{\text{T}}$$\therefore\frac{\text{v}_\text{T}}{\text{v}_0}=\sqrt{\frac{\text{T}_\text{T}}{\text{T}_0}}=\sqrt{\frac{\text{T}_\text{T}}{273}}$
But it is given, $\frac{\text{v}_\text{T}}{\text{v}_0}=\frac{3}{1}$$\Rightarrow\frac{3}{1}=\sqrt{\frac{\text{T}_\text{T}}{\text{T}_0}}\Rightarrow\frac{\text{T}_\text{T}}{273}=9$
$\therefore\text{T}_\text{T}=273\times9=2457\text{k}$
$=2457-273=2184^\circ\text{C}$

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Question 22 Marks

When two waves of almost equal frequencies $n_1$ and $n_2$ reach at a point simultaneously, what is the time interval between successive maxima?

Answer

If two waves of almost equal frequencies interfere, they are producing beats.Let $\text{n}_1>\text{n}_2$
Beat frequency $\text{f}_\text{beat}=\text{n}_1-\text{n}_2$
$\therefore$ Time period of beats $\text{T}_\text{beats}=\frac{1}{\text{f}_\text{beat}}=\frac{1}{\text{n}_1-\text{n}_2}$
This time period will be wqual to the time interval between successive mixima.

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Question 32 Marks

Given below are some functions of x and t to represent the displacement of an elastic wave.$\text{y}=10\cos[(252-250)\pi\text{t}]\cos[(252+250)\pi\text{t}]$

Answer

Beats involve $(\text{v}_1+\text{v}_2)$ and $(\text{v}_1-\text{v}_2)$ so beats can be represented by$\text{y}=10\cos[(252-250)\pi\text{t}]$ represents beat so (c) (iii).

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Question 42 Marks

In the given progressive wave $\text{y}=5\sin(100\pi\text{t+0.4x})$ where y and x are in m, t is in s. What is the:
Wave length

Answer

Standard form of progressive wave travelling in $+\text{x}$ direction (kx and $\omega\text{}t$ have opposite sign is given) Eqn. is $\text{y}=\text{a}\sin(\omega\text{t}-\text{kx}+\phi)$$\text{y}=5\sin(100\pi\text{t}-0.4\pi\text{t}+0)$
Wavelength $\lambda,\text{k}=\frac{2\pi}{\lambda}$$\text{k}=0.4\pi$
$\lambda=\frac{2\pi}{\text{k}}=\frac{2\times\pi}{0.4\pi}=5\text{m}$

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Question 52 Marks

Given below are some functions of x and t to represent the displacement of an elastic wave.$\text{y}=5\cos(4\times)\sin(20\text{t})$

Answer

A travelling wave along (-x) direction must have $+\text{kx}\ \text{i}.\text{e}.,$ in $(\text{iv})\text{y}=100\cos(100\pi\text{t}+0.5)$ so (a) (iv).

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Question 62 Marks

For the harmonic travelling wave $\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x}+3.5)$ where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of:
4m

Answer

$\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x+3.5})$$\text{y}=2\cos(20\pi\text{t}-0.0016\pi\text{x}+7.0\pi)$
Wave is propagated in $+\text{x}$ direction because $\omega\text{t}$ and kx are in with opposite sign standard equation $\text{y}=\text{a}\cos(\omega\text{t}-\text{kx}+\phi)$
a = 2, $\omega=20\pi,\ \text{k}=0.016\pi$ and $\phi=7\pi$
Path difference p =4 m (given) = 400cm
Phase difference $\Delta\phi=\frac{2\pi}{\lambda}\times\text{p}=\frac{2\pi}{\lambda}\times400$
$\Delta\phi=\text{k}\times400=0.016\pi\times400$
Phase difference $\Delta\phi=6.4\pi$ rad.

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