Beat Frequency

Q. A tuning fork vibrating with a sonometer having $20cm$ wire produces $5$ beats per second. If the beat frequency does not change if the length of the wire is changed to $21cm$, then the frequency of the tuning fork $($in $Hz)$ must be

1. $200$
2. $210$
3. $205$
4. $215$

Q. In a guitar, two strings $A$ and $B$ made up of the same material produce beats of frequency $4\text{Hz}$. When the tension in $B$ is slightly decreased, the beat frequency increases to $6\text{Hz}$. If the frequency of $A$ is $530\text{Hz}$ then the original frequency of $B$ will be

1. $526\text{Hz}$
2. $542\text{Hz}$
3. $546\text{Hz}$
4. $530\text{Hz}$

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

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

Q. Two vibrating tuning forks produce waves given by $y_1=4\sin 500\pi t$ and $y_2=2\sin 506\pi t$. Number of beats produced per minute is

1. $360$
2. $180$
3. $60$
4. $3$

Q. Two factories are sounding their sirens at 800 Hz. A man goes from one factory to the other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in 1 s will be

1. 2
2. 4
3. 8
4. 10

Q. An air column at temperature of ${51}^{\circ }\text{C}$ produces $4$ beats in one second with a tuning fork.
When the temperature of the air column decreases to ${16}^{\circ }\text{C}$ then one beat per second is produced with same tuning fork. The frequency of the tuning fork is

1. $50\text{Hz}$
2. $80\text{Hz}$
3. $70\text{Hz}$
4. $60\text{Hz}$

Q. Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If the speed of sound is 340 m/s, what must be the value of u so that he hears
10 beats per second?

1. 2.0 m/s
2. 2.5 m/s
3. 30 m/s
4. 3.5 m/s

Q. $25$ tuning forks are arranged in decreasing order of frequency. Any two successive forks produce $3$ beats/sec. If the frequency of the first tuning fork is the octave of last, then the frequency of ${21}^{st}$ fork is

1. $72\text{Hz}$
2. $288\text{Hz}$
3. $84\text{Hz}$
4. $87\text{Hz}$

Q.

A tuning fork produces 4 beats per second with another tuning fork of frequency 256 Hz. The first one is now loaded with a little wax and the beat frequency is found to increase to 6 per second. What was the original frequency of the tuning fork?

Q.

A bus is moving with a velocity of 5 m/s towards a huge wall. the driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 355 m/s, the number of beats heard per second by a passenger on the bus will be approximately,

1. 6

2. 5

3. 4

4. 3

Q. It we study the vibration of a pipe open at both ends, then the following statement is not true -

1. Open end will be an antinode
2. Odd harmonics of the fundamental frequency will be generated
3. All harmonics of the fundamental frequency will be generated
4. Pressure change will be maximum at both ends

Q. A tuning fork $A$ of unknown frequency produces $4$ beats per second when sounded with another tuning fork $B$ of frequency $254\text{Hz}$. When tuning fork $A$ is loaded with wax, it still gives $4$ beats per second with tuning fork $A$. The initial unknown frequency of tuning fork $A$ is

1. $258\text{Hz}$
2. $254\text{Hz}$
3. $250\text{Hz}$
4. $262\text{Hz}$

Q.

Define frequency

Q.

A pipe of length $85cm$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250Hz$. The velocity of sound in air is $340\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

1. $12$

2. $8$

3. $6$

4. $4$

Q. A person observes two trains one of them is coming towards with speed of $4\text{m/sec}$ and another is going away with same speed. If the two trains blowing a whistle with frequency $240\text{Hz}$. The beat frequency heard by stationary person will be (speed of sound in air $=320\text{m/sec}$.)

1. zero
2. $6$
3. $12$
4. $3$

Q. An observer moves towards a stationary source of sound with a speed ($1/5$)th of the speed of sound. The wavelength and frequency of the sound emitted are $\lambda$ and $f$ respectively. The apparent frequency and wavelength recorded by the observer are, respectively:

1. $1.2f$ and $\lambda$
2. $f$ and $1.2\lambda$
3. $0.8f$ and $0.8\lambda$
4. $1.2f$ and $1.2\lambda$

Q. A particle executes SHM with a frequency f. the frequency with which it KE oscillates is? 1) f/2 2) f. 3) 2f. 4) 4f

Q. When two tuning forks, fork $A$ and fork $B$ are sounded together, $4$ beats per second are heard. When the tuning fork $B$ is loaded with wax then $6$ beats per second are heard. If the frequency of fork $A$ is $200\text{Hz}$ then what was the original frequency of fork $B$?

1. $196\text{Hz}$
2. $200\text{Hz}$
3. $209\text{Hz}$
4. $202\text{Hz}$

Q. Two tuning forks have frequencies 450 Hz and 454 Hz respectively. On sounding these forks together, the time interval between successive maximum intensities will be

1. 1 sec
2. 2 sec
3. 1/4 sec
4. 1/2 sec

Q.

An air column in a pipe, which is closed at one end, will be in resonance with a vibrating body of frequency 166 Hz, if the length of the air column is

1. 0.50 m

2. 2.00 m

3. 1.50 m

4. 1.00 m

Q. Wavelength of two notes in air are $\left(\frac{90}{175}\right)mand\left(\frac{90}{173}\right)m$, respectively. Each of these notes produces 4 beats per second with a third note of a fixed frequency. Calculate the velocity of sound in air in m/s.

1. 420
2. 460
3. 360
4. 320

Q. The tuning forks A and B produce notes of frequency $256$ Hz and $262$ Hz respectively. An unknown note sounded at the sametime as A produces beats. When the same note is sounded with B, beat frequency is twice as large. The unknown frequency could be:

1. 268 Hz
2. 250 Hz
3. 260 Hz
4. None of these

Q. Assertion: When two vibrating tuning forks having frequencies $256\text{Hz}$ and $212\text{Hz}$ are held near each other then beats cannot be heard.
Reason: The principle of superposition is valid only if the frequencies of the oscillators are nearly equal.

1. Assertion and reason both are correct.
2. Assertion and reason both are wrong
3. Assertion is correct while reason is wrong
4. Assertion is wrong while reason is correct.

Q. When tuning forks $A$ and $B$ are sounded together, $5$ beats per second are heard. The frequency of $A$ is $250\text{Hz}$. On loading fork $A$ with wax, $2$ beats per second are produced with fork $B$. The frequency of fork $B$ is -

1. $255\text{Hz}$
2. $320\text{Hz}$
3. $245\text{Hz}$
4. $420\text{Hz}$

Q. Two sound waves with wavelengths $5\text{m}$ and $5.5\text{m}$ respectively, propagates in a gas with velocity $330\text{m/s}$. The number of beats per second will be

1. $6\text{Hz}$
2. $15\text{Hz}$
3. $17\text{Hz}$
4. $19\text{Hz}$

Q.

A musical instrument is made using four different metal strings. $1,2,3$ and 4 with mass per unit length $\mu ,2\mu ,3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L_0\text{and}2L_0\text{. It is found that in string-}1\text{(}\mu )$ at free length $L_0$ and tension $T_0$ the fundamental mode frequency is $f_0.$ List-I gives the above four strings while List-II lists the magnitude of some quantity.

	List-I		List-II
(i)	String-1$\left(\mu \right)$	(P)	$1$
(ii)	String-2$\left(2\mu \right)$	(Q)	$1/2$
(iii)	String- 3$\left(3\mu \right)$	(R)	$1/\sqrt{2}$
(iv)	String-4$\left(4\mu \right)$	(S)	$1/\sqrt{3}$
		(T)	$3/16$
		(U)	$1/16$

If the tension in each string is $T_0$, the correct match for the highest fundamental frequency in $f_0$ units will be,

1. $I\to P,II\to R,III\to S,IV\to Q$

2. $I\to Q,II\to P,III\to R,IV\to T$

3. $I\to Q,II\to S,III\to R,IV\to P$

4. $I\to P,II\to Q,III\to T,IV\to S$

Q. The frequency of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of tuning fork $C$. When
$A$ and $B$ are simultaneously excited, $5$ beats per second are produced. Then the frequency of the tuning fork $A$ (in $Hz$) is

Q. Two waves are represented by $Y_1=4\sin 404\pi t$ and $Y_2=3\sin 400\pi t$. Then:

1. Beat frequency is $4\text{Hz}$ and the ratio of maximum to minimum intensity is $49:1$
2. Beat frequency is $2\text{Hz}$ and the ratio of maaximum to minimum intensity is $49:1$
3. Beat frequency is $2\text{Hz}$ and the ratio of maximum to minimum intensity is $7:1$.
4. Beat frequency is $4\text{Hz}$ and the ratio of maximum to minimum intensity is $7:1$

Q. Three sound waves of equal amplitudes have frequencies $(n–1),n,(n+1)$. They superimpose to give beats. The number of beats produced per second will be

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

Q. The frequency of tuning forks $A$ and $B$ are respectively $3\%$ more and $2\%$ less than the frequency of the tuning fork $C$. When $A$ and $B$ are simultaneously excited then $5$ beats per second are produced. The frequency of the tuning fork $A$ is

1. $103\text{Hz}$
2. $109\text{Hz}$
3. $107\text{Hz}$
4. $105\text{Hz}$