Resonance in Sound Waves

Q. A string of length $l$ is fixed at both ends. It is vibrating in its $3^{rd}$ overtone with maximum amplitude $a$. The amplitude at a distance $\frac{l}{3}$ from one end is

1. $a$
2. $0$
3. $\frac{\sqrt{3}a}{2}$
4. $\frac{a}{2}$

Q. A train is moving on a straight track with speed $20m{s}^{-1}$. It is blowing its whistle at the frequency of 1000Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is close to:

1. 6%
2. 12%
3. 24%
4. 18%

Q. A simple harmonic motion is represented by:

$y=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)\text{cm}$

The amplitude and time period of the motion are:

1. $5\text{cm},\frac{3}{2}\text{s}$
2. $10\text{cm},\frac{3}{2}\text{s}$
3. $5\text{cm},\frac{2}{3}\text{s}$
4. $10\text{cm},\frac{2}{3}\text{s}$

Q. In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of $20.0cm$ for a tuning fork of frequency $400Hz$ is used. The velocity of the sound at room temperature is $336m{s}^{–1}$. The third resonance is observed when the air column has a length of cm

Q. Which of the following circuits provide full-wave rectification of an a.c. input ?

1. 
2. 
3. 
4. 

Q. If a tuning fork of frequency $\left(f_0\right)=340Hz$ and tolerance $\pm 1\%$ is used in resonance column method, the first and the second resonance are measured at ${\ell }_1=24.0cmand{\ell }_2=74.0cm$. Find maximum permissible error in speed of sound.

1. 1.8%
2. 1%
3. 1.2%
4. 1.4%

Q. A string on a musical instrument is 50 cm long and its fundamental frequency is 270 Hz. If the desired frequency of 1000 Hz is to be produced, the required length of the string is

1. 2.7 cm
2. 5.4 cm
3. 13.5 cm
4. 10.3 cm

Q. Two vectors of the same physical quantity are equal if

1. they have the same magnitude and the same direction.
2. they have different magnitudes but the same direction.
3. they have the same magnitude but different directions.
4. they have different magnitudes and different directions.

Q. A closed organ pipe of length $1.2\text{m}$ vibrates in its first overtone mode. The pressure variation is maximum at :
[neglect end correction]

1. $0.4\text{m}$ from the open end
2. $0.4\text{m}$ from the closed end
3. Both (a) and (b)
4. $0.8\text{m}$ from the open end

Q.

On applying forced vibrations, the resonance wave becomes very fast when

Q.

A Kundt's tube apparatus has a copper rod of length 1.0 m clamped at 25 cm from one of the ends. The tube contains air in which the speed of sound is 340 in/s. The powder collects in heaps separated by a distance of 5.0 cm. Find the speed of sound waves in copper.

Q. A tuning fork of frequency $200\text{Hz}$ is vibrating with a sonometer wire to produce $10\text{beats/sec}$. When the tension in the sonometer wire is increased, beat frequency decreases. Original frequency of the sonometer wire in $\text{Hz}$ is

Q.

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude $P_A$ inside the tube. If the atmospheric pressure is $P_0$ then the ratio of maximum and minimum pressure at the closed end of the tube will be

1. $\frac{P_A+P_0}{P_A-P_0}$

2. $\frac{P_A+2P_0}{P_A-2P_0}$

3. $\frac{P_A}{P_0}$

4. ($\frac{P_A+\frac{1}{2}{P}_0}{P_A-\frac{1}{2}{P}_0}$)

Q.

Two successive resonance frequencies in an open organ pipe are 1620 Hz and 2268 Hz. Find the length of the tube. The speed of sound in air is $324m{s}^{-1}$.

Q. A resonance air column of length 20 cm resonates with a tuning fork of frequency 250 Hz. The speed of sound in air is

1. 300 m/s
2. 200 m/s
3. 150 m/s
4. 75 m/s

Q.

What is meant by natural vibration?

Q. A student performs an experiment on photoelectric effect, using two materials $A$ and $B$. A plot of $V_{stop}$ vs $v$ is given in Figure.


A Which material $A$ or $B$ has a higher work function?

B Given the electric charge of an electron $=1.6\times {10}^{-19}C$, find the value of $h$ obtained from the experiment for both $A$ and $B$? Comment on whether it is consistent with Einstein’s theory:

Q. All physical quantities are classified into vectors and scalars.

1. True
2. False

Q.

A boy riding on a bicycle going at 12 km $h^{-1}$ towards a vertical wall whistles at his dog on the ground. If the frequency of the whistle is 1600 Hz and the speed of sound in air is $330m{s}^{-1}$, find (a) the frequency of the whistle as received by the wall (b) the frequency of the reflected whistle as received by the boy.

Q. A half-wave rectifier is used to supply 10V DC to a resister load of 100 Ω. If the forward resistance of diode is 25 Ω. Then the value of AC voltage supplied to the circuit is

Q.

Two closed organ pipe $\mathrm{A}$ and $\mathrm{B}$ have the same length. $\mathrm{A}$ is wider than $\mathrm{B}$. They resonate in the fundamental mode at frequencies ${\mathrm{v}}_{\mathrm{A}}$ and ${\mathrm{v}}_{\mathrm{B}}$ respectively, then

1. ${\mathrm{v}}_{\mathrm{A}}={\mathrm{v}}_{\mathrm{B}}$

2. ${\mathrm{v}}_{\mathrm{A}}>{\mathrm{v}}_{\mathrm{B}}$

3. ${\mathrm{v}}_{\mathrm{A}}<{\mathrm{v}}_{\mathrm{B}}$

4. either (2) or (3) depending on the ratio of their diameters

Q. A sonometer wire vibrating in first overtone has length of 31.25 cm. Tension in the wire is 256 N and mass per unit length is $\frac{10gm}{m}$. When it is sounded together with a tuning fork, 10 beats are heard. If tension in the wire is slightly changed, no beats are heard. What is the possible frequency of the tuning fork?

1. 502 Hz
2. 510 Hz
3. 505 Hz
4. None of these

Q.

Resonance is an example of

1. tuning fork
2. forced vibration
3. damped vibration
4. free vibration

Q.

A U-tube having unequal arm-lengths has water in it. A tuning fork of frequency 440 Hz can set up the air in the shorter arm in its fundamental mode of vibration and the same tuning fork can set up the air in the longer arm in its first overtone vibration. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air =$330m{s}^{-1}$.

Q.

Where can a body execute the free vibrations?

Q. A tuning fork of frequency $500\text{Hz}$ is sounded on a resonance tube. The first and second resonances are obtained at $17\text{cm}$ and $52\text{cm}.$ The velocity of sound is

1. $170\text{m/s}$
2. $350\text{m/s}$
3. $520\text{m/s}$
4. $850\text{m/s}$

Q.

Consider the situation shown in figure. The wire which has a mass of 4.00 g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming that the speed of sound in air is 340 $m{s}^{-1}$, find the tension in the wire.

1. 11.6N

2. 8 N

3. 340N

4. None of these

Q. The number of possible natural oscillations of air column in a pipe closed at one end of length $85cm$ whose frequencies lies below $1250Hz$ are:
(velocity of sound $=340m{s}^{-1}$)

1. $4$
2. $5$
3. $7$
4. $6$

Q. A string clamped at both ends is vibrating in the 3rd harmonic. Then, the total number of antinodes is

1. 3
2. 4
3. 2
4. 5

Q.

State two ways in which resonance differs from forced vibrations.