Frequency

Q.

A wheel is of diameter $1\mathrm{m}$. If it makes $30\mathrm{revolutions}/\sec$, then the linear speed (in m/sec) of a point on its circumference is:

1. $30\mathrm{\pi }$

2. $\mathrm{\pi }$

3. $60\mathrm{\pi }$

4. $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Q. The period of oscillation of a simple pendulum in the experiment is recorded as $2.63s$, $2.56s$, $2.42s$, $2.71s$ and $2.80s$ respectively. The average absolute error is

1. $0.11s$
2. $0.01s$
3. $1.0s$
4. $0.1s$

Q. A radio station broadcasts on a carrier frequency of $100\text{MHz}$. The wavelength of this radio wave is most nearly

1. $3\text{m}$
2. $30\text{m}$
3. $300\text{m}$
4. $0.3\text{m}$

Q.

If two tuning forks $A$ and $B$ are sounded together, they produce $4$ beats per second. $A$ is then slightly loaded with wax, they produce $2$ beats when sounded again. The frequency of $A$ is $256$. The frequency of $B$ will be

1. $250$
2. $260$
3. $262$
4. $252$

Q. Two tuning forks when sounded together produced $4$beats/sec. The frequency of one fork is $256Hz$. The number of beats heard increases when the fork of frequency $256Hz$ is loaded with wax. The frequency (in $Hz$) of the other fork is

Q. In a resonance pipe the first and second resonances are obtained at depths $22.7cm$ and $70.2cm$ respectively. What will be the end correction (in $cm$)?

Q.

A man is standing on a railway platform listening to the whistle of an engine that passes the man at constant speed without stopping. If the engine passes the man at time $t_0$. How does the frequency $f$ of the whistle as heard by the man changes with time

1. 
2. 
3. 
4. Diagram

Q. An open pipe of length $33cm$ resonates to a frequency of $1000Hz$. The mode of vibration is $(\text{velocity of sound}=330m/s$)

1. The $4^{th}$ harmonic
2. The $2^{nd}$ harmonic
3. The $3^{rd}$ harmonic
4. Fundamental

Q.

What do you understand by the term resonance? Give two conditions for producing resonance.

Q. A string $2.0m$ long and fixed at its ends is driven by a $240Hz$ vibrator. The string vibrates in its $\text{third}$ harmonic mode. The speed of the wave and its fundamental frequency is

1. $320m/s,80Hz$
   
2. $320m/s,120Hz$
   
3. $180m/s,120Hz$
   
4. $180m/s,80Hz$
   

Q. The mass per unit length of a rod of length $3$ $m$ is directly proportional to distance $x$ from its one end. The centre of mass of the rod from that end will be at

1. $1.5\text{m}$
2. $2.5\text{m}$
3. $3\text{m}$
4. $2\text{m}$

Q. A progressive wave equation is given as: $y=0.5\sin (10\pi t-5x)$, where $x$ and $y$ are 𝑖𝑛 $cm$ and $t$ is in $\text{second}$. The maximum velocity $\left(\text{in}cm/s\right)$ of the particle is $x\pi$. Find $x$.

Q. The equation
$y=A{\cos }^2(2\pi nt-2\pi \frac{x}{\lambda })$ represents a wave with

1. Amplitude $A$, frequency $n$ and wavelength $\lambda$
2. Amplitude $A/2$, frequency $2n$ and wavelength $\lambda$
3. Amplitude $A/2$, frequency $2n$ and wavelength $\lambda /2$
4. Amplitude $A$, frequency $2n$ and wavelength $2\lambda$

Q.

A periodic wave is characterized by

1. frequency only

2. amplitude only

3. time period only

4. all the above

Q. 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?

Q. A submarine $\left(A\right)$ travelling at $18{\text{Km hr}}^{-1}$ is being chased along the line of its velocity by another submarine $\left(B\right)$ travelling at $27{\text{Km hr}}^{-1}$. $B$ sends a sonar signal of $500\text{Hz}$ to detect $A$ and receives a reflected sound of frequency $\nu$ . The value of $\nu$ is close to :
$(\text{Speed of sound in water}=1500{\text{ms}}^{-1}$)

1. $504\text{Hz}$
2. $507\text{Hz}$
3. $499\text{Hz}$
4. $502\text{Hz}$

Q. The frequency of a man's voice is $300Hz$ and its wavelength is $1meter$. If the wavelength of a child's voice is $1.5m$, then the frequency (in $Hz$ ) of the child's voice is:

Q. The angular frequency of motion whose equation is $9\frac{d^{2}y}{d{t}^2}+16y=0$ is

$(y$ is displacement and $t$ is time$)$

1. $\frac{9}{4}\text{units}$
2. $\frac{4}{9}\text{units}$
3. $\frac{4}{3}\text{units}$
4. $\frac{2}{3}\text{units}$

Q.

Why does microwave oven heat up a food item containing water molecules most efficiently?

Q. A tuning fork whose frequency as given by manufacturer is $512Hz$ is being tested with an accurate oscillator. It is found that the fork produces a beat of $2Hz$ when oscillator reads $514Hz$ but produces a beat of $6Hz$ when oscillator reads $510Hz$. The actual frequency of fork is

1. $516Hz$
2. $518Hz$
3. $508Hz$
4. $512Hz$

Q. In a sinusoidal wave, the time required for a particle to move from maximum displacement to mean position is $0.17\text{s}$. The frequency of the wave is

1. $1.47\text{Hz}$
2. $0.92\text{Hz}$
3. $2.94\text{Hz}$
4. $4.17\text{Hz}$

Q. A stretched string of $1\text{m}$ length fixed at both ends, having a mass of $5\times {10}^{-4}\text{kg}$ is under a tension of $20\text{N}$. It is plucked at a point situated at $25\text{cm}$ from one end. The stretched string would vibrate with a frequency of

1. $100\text{Hz}$
2. $200\text{Hz}$
3. $400\text{Hz}$
4. $256\text{Hz}$

Q. When a tuning fork $A$ of unknown frequency is sounded with another tuning fork $B$ of frequency $256Hz$, then $3$ beats per second are observed. After that $A$ is loaded with wax and sounded, the again $3$ beats per second are observed. The frequency of the tuning fork $A$ is

1. $250Hz$
2. $262Hz$
3. $259Hz$
4. $253Hz$

Q.

A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statement about the velocity of the car is true

1. Magnitude of velocity is not constant

2. Both magnitude and direction of velocity change

3. Velocity is directed towards the centre of the circle

4. Magnitude of velocity is constant but direction changes

Q. A train is passing by a platform at a constant speed of $40m/s$. The train horn is sounded at a frequency of $378Hz$. Find the overall change in frequency (in $Hz$) as detected by a person standing on the platform, as the train moves from approaching to receding. (Take velocity of sound in air as $320m/s$)

Q. At each of two stations $A$ and $B$, a siren is sounding with a constant frequency of $250\text{cycle}/s$. A cyclist from $A$ proceeds straight towards $B$ with a velocity of $12km/h$ and hears $5\text{beats}/s$. The velocity of sound is nearly:

1. $336m/s$
2. $320m/s$
3. $328m/s$
4. $333m/s$

Q.

A water wave traveling in a straight line on a lake is described by the equation.

$y(x,t)=3.75cmcos(0.450c{m}^{-1}x+5.40s^{-1}t)$

where y is the displacement perpendicular to the undisturbed surface of the lake. How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor?

1. 1.16s

2. 3.48s

3. 2.32s

4. 4.64s

Q.

Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

Q.

Time period of vibration of a particle is $0.25s$. Calculate the frequency.

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

$A$: $4m$

$B$: $0.5m$

$C$: $\lambda /2$

$D$: $\frac{3\lambda }{4}$ (At a given instant of time)

$E$: What is the phase difference between the oscillation of a particle located at $x=100cm,\text{at}t=Ts\text{and}t=5s$?