2 Marks Questions

Question 512 Marks

Explain your answers.
What is the amplitude of a point 0.375m away from one end?

Answer

Amplitude at a point x = 0.375m will be obtained by putting $\cos(120\pi\text{ t})$ as + 1 in the wave equation
$\therefore\ \text{A(x)}=0.06\sin\Big(\frac{2\pi}{3}\times0.375\Big)\times1=00.06\sin\frac{\pi}{4}=0.042\text{m}$

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Question 522 Marks

A steel wire has a length of 12.0m and a mass of 2.10kg. What should be the tension in the wire so that the speed of transverse wave on the wire equals the speed of sound in dry air at 20°C? Take the speed of sound at 20°C = 343m/s.

Answer

$\text{l}=12\text{m}$ and $\text{M}=2.10\text{kg}$
$\therefore\mu=\frac{2.10}{12}=0.175\text{kg/m}$
and $\text{v}=343\text{m/s}$
Using, $\text{v}=\sqrt{\frac{\text{T}}{\mu}}$
$\text{T}=\text{v}^2\mu=(343)^2\times0.175$
$=20.5\times10^4\text{N}$

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Question 532 Marks

The intensity maxima due to two interfering waves of equal amplitude a₁ = a₂ = a is 4a². Does this violate the law of conservation of energy? Justify.

Answer

No, The average intensity of maxima and minima will be, $\text{I}_{\text{av}}=\frac{4\text{a}^2+0}{2}=2\text{a}^2,$ which is the sum of their intensities.
So, energy conservation is obeyed, but redistribution of energy has taken place.

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Question 542 Marks

Define temperature coefficient of the velocity of sound.

Answer

The temperature coefficient of the velocity of sound is defined as the change in the velocity of sound, when the temperature changes by 1°C (or 1K). It is denoted by $\alpha.$

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Question 552 Marks

In an experiment, it was found that a tuning fork and a sonometer wire gave 5 beats per second, both when the length of the wire was 1m, and 1.05m. Calculate the frequency of the fork.

Answer

We know $\text{v}=\frac{1}{2\text{l}}\sqrt{\frac{\text{T}}{\mu}}$
I case: $\text{v}_1=\frac{1}{2\times1}\sqrt{\frac{\text{T}}{\mu}}\ ... (\text{i})$
II case: $\text{v}_2=\frac{1}{2\times1.05}\sqrt{\frac{\text{T}}{\mu}}\ ...\text{(ii)}$
Let v be the frequecy of the tuning fork, therefore,
$\text{v}_1-\text{v}=5$ and $\text{v}-\text{v}_2=5$
$\text{v}_1=\text{v}+5$
and $\text{v}_2=\text{v}-5$
$\frac{\text{v}_1}{\text{v}_2}=\frac{5+\text{v}}{\text{v}-5}$
From (i) and (ii), we have
$\frac{\text{v}+5}{\text{v}-5}=\frac{1}{2}\times2\times1.05=1.05$
$\frac{\text{v}+5}{\text{v}-5}=\frac{105}{100}=\frac{21}{20}$
$\Rightarrow\text{v}=205\text{Hz}$

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Question 562 Marks

What travels faster-a rifle bullet or the sound of a shot?

Answer

Rifle bullet travels faster than the sound of shot. The ratio of v_b and v_s is nearly 3 : 1.

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Question 572 Marks

The transverse displacement of a string (clamped at its both ends) is given by
$\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\text{x}\Big)\cos(120\pi\text{ t})$
where x and y are in m and t in s. The length of the string is 1.5m and its mass is 3.0 × 10^–2kg.
Answer the following:
Does the function represent a travelling wave or a stationary wave?

Answer

The general equation representing a stationary wave is given by the displacement function:
$\text{y}(\text{x, t})=2\text{a}\sin\text{kx}\cos\omega\text{t}$
This equation is similar to the given equation:
$\text{y}(\text{x, t})=0.06\sin\Big(\frac{2}{3}\text{x}\Big)\cos(120\pi\text{ t})$
Hence, the given function represents a stationary wave.

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Question 582 Marks

If the frequency of a tuning fork is 400Hz and the velocity of sound in air is 320m/s, find how far does the sound travel when the fork executes 30 vibrations.

Answer

$\text{v}=320\text{m/s};$
$\text{v}=400\text{Hz};$
$\lambda=\frac{\text{v}}{\text{v}}=\frac{320}{400}=0.8\text{m}$
$\therefore$ The required distance travelled during the time the fork makes 30 vibrations = 30 × 0.8 = 24m.

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Question 592 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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Question 602 Marks

A child blows air at one end of a straw and slowly cuts pieces of the straw from the other end. What will be the outcome that will be observed?

Answer

As the pipe gets cut, the length of the resonating column varies, and so at a particular length, there will be an audible frequency that will be heard.

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Question 612 Marks

Show graphically, the intensity variation of beats formation?

Answer

When beats are formed by two sources having same amplitude but slightly different frequencies, the amplitude is given by $2\text{A}\cos2\pi\text{v}_\text{m}\text{t}$ where $\text{v}_\text{m}=\frac{\text{v}_1-\text{v}_2}{2}.$ Intensity $=4\text{A}^2\cos^2(2\pi\text{v}_\text{m}\text{t})$ and is shown graphically here.

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Question 622 Marks

If oil of density higher than that of water is used in place of water in a resonance tube, how does the frequency change?

Answer

The frequency is governed by the air column and does not depend upon the nature of the liquid. So frequency would not change.

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Question 632 Marks

What is the condition to be obeyed for receiving an echo?

Answer

The separation between the reflecting surface and source of sound ‘d’ should be greater than $\Big(\frac{1}{20}\Big)^{\text{th}}$ of the velocity of sound, since persistence of sound in human ears is $\frac{1}{10}\text{sec}.$

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Question 642 Marks

An observer at a sea-coast observes waves reaching the coast. What type of waves does he observe? Why?

Answer

Elliptical waves while the waves on the surface of water are transverse, the waves just below the surface of water are longitudinal. So the resultant waves are elliptical.

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Question 652 Marks

The frequencies of the two tuning forks A and B are 250Hz and 255Hz respectively. Both are sounded together. How many beats will be heared in 5s?

Answer

Given: v_A = 250Hz, v_B = 255Hz, t = 5s
v_B - v_A = 255Hz - 250Hz = 5Hz = Beat frequency
$\therefore$ No. of beats heard in 5s = 5 × 5 = 25

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Question 662 Marks

Does a vibrating source always produce sound?

Answer

A vibrating source produces sound when it vibrates in a medium and frequency of vibration lies within the audible range (20Hz to 20kHz).

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Question 672 Marks

Why do we not hear beats if the frequency of two sounds are widely different?

Answer

The beats cannot be heard due to persistence of hearing if the difference in frequencies is more than 10.

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Question 682 Marks

What is the physical reason to take both +1 and -1 as the cosine maxima in beats formation?

Answer

Since Intensity $\propto$ (Amplitude)², both +1 and -1 are to be considered in beats.

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Question 692 Marks

Two sound sources produce 20 beats in 5s. By how much do their frequencies differ?

Answer

Number of beats per second $=\frac{20}{5}=4$
$\therefore \text{V}_1-\text{V}_2=4.$

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Question 702 Marks

What is the ratio of frequencies of fundamental tone and various overtones formed in a vibrating string?

Answer

The frequencies of various harmonics (or fundamental tone and overtones) in vibrating string are in the ratio:
V₁ : V₂ : V₃..... = 1 : 2 : 3 : 4......

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Question 712 Marks

Define the terms 'node' and 'antinode'?

Answer

Node: It is a point on stationary wave at which amplitude of vibration of the particle is zero.
Antinode: It is a point on stationary wave at which amplitude of vibration of the particle is maximum.

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Question 722 Marks

An open pipe resonates with a frequency v. When half of it is immersed in a dense liquid, what is the fundamental frequency?

Answer

$\text{V}=\frac{\nu}{2\text{l}}$ with fundamental frequency. When half immersed in a denser liquid, it will act as a closed pipe of length $\frac{\text{l}}{2}.$
$\therefore \text{V}'=\frac{\nu}{4\text{l}'}=\frac{\nu}{\frac{4\text{l}}{2}}=\frac{\nu}{2\text{l}}$
So, V = V'

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Question 732 Marks

If a balloon is filled will CO₂ gas, then how can it behave as a lens for sound waves? If it was filled with hydrogen gas, then what will happen?

Answer

Velocity of sound in CO₂ is less than that in air. Therefore, balloon will behave as a convex lens for sound waves. In hydrogen, velocity of sound is greater than that in air. Therefore, balloon filled with hydrogen will behave as a concave lens.

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Question 742 Marks

Why do we see the flash of lightning first and hear the thunder later?

Answer

Since light travels much faster than sound, the flash of lightning is seen first, and the thunder is heard later.

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Physics 2 Marks Questions