Revisiting Standing Waves

Q. A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 $\mathring{A}$ between them. The wavelength of the standing wave is

1. 1.21 Å
2. 2.42 Å
3. 6.05 Å
4. 3.63 Å

Q. An aluminium rod having length $100\text{cm}$ is clamped at its middle point and set into longitudinal vibrations. Let the rod vibrate in its fundamental mode. The density of aluminium is $2600{\text{kg/m}}^3$ and its Young's modulus is $7.8\times {10}^{10}{\text{N/m}}^2.$ The frequency of the sound produced is

1. $1250\text{Hz}$
2. $2738\text{Hz}$
3. $2350\text{Hz}$
4. $1685\text{Hz}$

Q.

A one meter long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300m/s,$ the frequency difference between the fundamental and second harmonic of this pipe is __$Hz$.

Q.

Name the two types of mechanical waves.

Q.

A copper rod of length 1.0 m is clamped at its middle point. Find the frequencies between 20 Hz and 20, 000 Hz at which standing longitudinal waves can be set up in the rod. The speed of sound in copper is $3.8km{s}^{-1}$

1. None of these

2. $n\times 1.9kHz$

   $n=1,2,\mathrm{3.....}10$

3. $n\times 3.1kHz$

   $n=1,2,3,4,5,6$

4. $n\times 5kHz$

   $n=1,2,3,4$

Q. In a $YDSE$, a thin film $(\mu =1.6)$ of thickness $0.01\text{mm}$ is introduced in the path of one of the two interfering beams. The central fringe moves to a position occupied by the ${10}^{th}$ bright fringe earlier. The wave length of the wave is

1. $600\dot{\text{A}}$
2. $6000\dot{\text{A}}$
3. $60\dot{\text{A}}$
4. $660\dot{\text{A}}$

Q. A resonating column of air contains .

1. stationary longitudinal waves
2. stationary transverse waves
3. longitudinal progressive waves

Q.

If the end correction of an open pipe is 0.8 cm then the inner radius of that pipe will be

Q.

A sirens $60-$hole disc rotates at a steady speed of $360$revolutions per minute. The sound that is emitted is in tune with a frequency tuning fork.

1. $10\mathrm{Hz}$

2. $360\mathrm{Hz}$

3. $216\mathrm{Hz}$

4. $60\mathrm{Hz}$

Q.

In a standing wave pattern in a vibrating air column, nodes are formed at a distance of 4.0 cm. If the speed of sound in air is $328m{s}^{-1}$, what is the frequency of the source ?

Q. Figure shows a tube structure in which a sound signal is sent from one end and is received at the other end. The semicircular part has a radius of $10.0\text{cm}$. The frequency of the sound source can be varied electronically between $1000\text{Hz}$ and $4000\text{Hz}$. Find the approximate frequency(s) at which a maxima of intensity is detected.

[The speed of sound in air = $340{\text{ms}}^{-1}$]

1. $2110\text{Hz}$
2. $2980\text{Hz}$
3. $8940\text{Hz}$
4. $7840\text{Hz}$

Q.

The separation between a node and the next antinode in a vibrating air column is 25 cm. If the speed of sound in air is 340 $m{s}^{-1}$, find the frequency of vibration of the air column

1. 670 Hz

2. 340 Hz

3. 240 Hz

4. 575 Hz

Q. The velocity of an electromagnetic wave is parallel to

1. $\overrightarrow{B}\times \overrightarrow{E}$
2. $\overrightarrow{E}\times \overrightarrow{B}$
3. $\overrightarrow{E}$
4. $\overrightarrow{B}$

Q.

A piezoelectric quartz crystal of thickness $0.005\mathrm{m}$ is vibrating in resonance conditions. Calculate the fundamental frequency ${\mathrm{f}}_0$ for quartz.

$\left(\mathrm{\gamma }=8\times {10}^{10}{\mathrm{Nm}}^{-2}\mathrm{and}\mathrm{\rho }=2.65\times {10}^3{\mathrm{kg}}^{-3}\right)$ .

1. $55\mathrm{MHz}$

2. $0.55\mathrm{MHz}$

3. $5.5\mathrm{MHz}$

4. $5.5\mathrm{kHz}$

Q.

The velocity of matter waves are

1. Not constant

2. Constant

3. Greater than electromagnetic waves

4. Less than electromagnetic waves

Q.

A copper rod of length 1.0 m is clamped at its middle point. Find the frequencies between 20 Hz and 20, 000 Hz at which standing longitudinal waves can be set up the rod. The speed of sound in copper is $3.8km{s}^{-1}$.

Q. A steel rod of length $100cm$ is clamped at the middle. The frequency of the fundamental mode for the lognitudinal vibrations of the rod is
(Speed of sound is steel $=5km{s}^{-1}$)

1. $2kHz$
2. $2.5kHz$
3. $3kHz$
4. $1.5kHz$

Q. An aluminium rod having length $100\text{cm}$ is clamped at its middle point and set into longitudinal vibrations. Let the rod vibrate in its fundamental mode. The density of aluminium is $2600{\text{kg/m}}^3$ and its Young's modulus is $7.8\times {10}^{10}{\text{N/m}}^2.$ The frequency of the sound produced is

1. $1250\text{Hz}$
2. $2738\text{Hz}$
3. $2350\text{Hz}$
4. $1685\text{Hz}$

Q. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is

1. 25 kg
2. 5 kg
3. 12.5 kg
4. 1/25 kg

Q. A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound then the velocity of the car is

1. $\frac{v}{2}$
2. $\frac{v}{3}$
3. $\frac{v}{4}$
4. $\frac{v}{\sqrt{2}}$

Q. The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by $y=2\text{(cm)}\sin \left[\right(0.6{\text{cm}}^{-1}x\left]\cos \right[\left(500\pi {\text{s}}^{-1}\right)t].$
What is its length ?

1. $24.6\text{cm}$
2. $12.5\text{cm}$
3. $20.6\text{cm}$
4. $15.7\text{cm}$

Q. A $20\text{cm}$ long string having a mass of $1\text{g}$ is fixed at both the ends. The tension in the string is $0.5\text{N}$. The string is set into vibrations using an external vibrator of frequency $100\text{Hz}$. The separation between the successive nodes on the string will be

1. $4\text{cm}$
2. $5\text{cm}$
3. $6\text{cm}$
4. $7\text{cm}$

Q.

What will be the nature of wave in sound ?

Q.

explain types of waves.

Q. Consider the following statements regarding the experiment to the determine the velocity of sound in laboratory by resonance tube method.
1. The first resonance is obtained for the length $x_1$ of the air column
2. The second resonance is obtained for the length $x_2$ of the air column.
If $n$ be the frequency of the tuning fork then which is the correct relation ($v$ represents the velocity of sound) ?

1. $v=2n(x_1+x_2)$
2. $v=2n(x_1-x_2)$
3. $v=2n(x_2-x_1)$
4. $v=2n\left(x_1{x}_2\right)$

Q. State whether true or false :

Q. A sound wave of frequency $f$ travels horizontal to the right. It is reflected from a large vertical plane surface moving to left with a speed $v$. If the speed of sound in medium is $c$ then

1. The number of waves striking the plane surface per second is $f\left(\frac{c+v}{c}\right)$
2. The wavelength of reflected wave is $\frac{c}{f}\left(\frac{c-v}{c+v}\right)$
3. The frequency of the reflected wave is $f\left(\frac{c+v}{c-v}\right)$
4. The number of the beats heard by a stationary listner to the left of the reflecting surface is $\frac{vf}{c-v}$

Q. In stationary wave, the distance between a node and its adjacent antinode is __________.

1. $\lambda$
2. $\frac{\lambda }{4}$
3. $\frac{\lambda }{2}$
4. $2\lambda$

Q. Stationary waves are set up in air column. The velocity of sound in air is $330m/s$ and frequency is $165Hz.$ Then the distance between the nodes is

1. $2m$
2. $1m$
3. $0.5m$
4. $4m$

Q. A tuning fork of frequency v resonates with a closed organ pipe when the lengths of the shortest air columns are a and b respectively. The speed of sound in air is :

1. $v(a-b)$
2. $v\frac{(b-a)}{2}$
3. $2v(b+a)$
4. $2v(b-a)$