Beat Frequency

Q.

Find the unknown entries $a$, $b$, $c$, $d$, $e$, $f$ in the following distribution of heights of students in a class

Height (in $\mathrm{cm}$)	Frequency	Cumulative Frequency given
$150-155$	$12$	$a$
$155-160$	$b$	$25$
$160-165$	$10$	$c$
$165-170$	$d$	$43$
$170-175$	$e$	$48$
$175-180$	$2$	$f$
Total	$50$

Q. A guitar wire $A$ vibrates at a fundamental frequency $600\text{Hz}$. A second identical wire $B$ produces $6$ beats per second with it when the tension in $B$ is slightly less than that of $A$. Find the ratio of the tension in $A$ to the tension in $B$.

1. $0.98$
2. $1.25$
3. $1.02$
4. $0.75$

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 $B$. 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. When two tuning forks $A$ and $B$ are sounded together, the number of beats heard is $\nu$. The frequency of fork $A$ is $f$. If the prong of fork $B$ is loaded with a little wax, the number of beats decreases. The initial frequency of fork $B$ is

1. $f+\nu$
2. $f-\nu$
3. $f+2\nu$
4. $f-2\nu$

Q. Ten tuning forks are arranged in increasing order of frequency in such a way that any two consecutive tuning forks produce $4$ beats per second. The highest frequency is twice that of the lowest frequency. Possible highest and lowest frequencies are

1. $80\text{Hz}$ and $40\text{Hz}$
2. $100\text{Hz}$ and $50\text{Hz}$
3. $44\text{Hz}$ and $22\text{Hz}$
4. $72\text{Hz}$ and $36\text{Hz}$

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

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. A tuning fork $A$ when sounded with a tuning fork $B$ of frequency $480\text{Hz}$ produces $5$ beats per second. When the prongs of $A$ are loaded with wax, it gives $3$ beats per second. The original frequency of the tuning fork $A$ is:

1. $475\text{Hz}$
2. $485\text{Hz}$
3. $483\text{Hz}$
4. $477\text{Hz}$

Q. In a resonance column experiment, a tuning fork of frequency $400\text{Hz}$ is used. The first resonance is observed when the air column has a length $20.0\text{cm}$ and the second resonance is observed when the air column has a length of $62.0\text{cm}$. Find the distance above the open end where the pressure node is formed ?

1. $1.5\text{cm}$
2. $3\text{cm}$
3. $2\text{cm}$
4. $1\text{cm}$

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?

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

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

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. 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. 1
4. 4

Q. Two sound sources are moving in opposite directions with velocities $v_1$ and $v_2(v_1>v_2)$. Both are moving away from a stationary observer. The frequency of both the sources is 900 Hz. What is the value of $v_1–v_2$ so that the beat frequency observed by the observer is 6 Hz? Speed of sound v = 300 m/s. Given that $v_1$ and $v_2$ ≪ v.

1. 1 m/s
2. 2 m/s
3. 3 m/s
4. 4 m/s

Q. A stationary source emits sound of frequency $670\text{Hz}$. The sound is reflected by a car approaching the source with a speed of $2\text{m/s}$. The reflected signal is received by the source and superimposed with the original. What will be beat frequency of the resultant signal in $\text{Hz}$?

(Given that the speed of sound in air is $340\text{m/s}$ and the car reflects the sound at the frequency it has received)

1. $8$
2. $15$
3. $25$
4. $12$

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. 3

4. 4

Q.

A tuning fork gives 4 beats with 50 cm length of a sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is

1. 396

2. 400

3. 404

4. 384

Q. Ten tuning forks are arranged in ascending order of their frequencies, each producing four beats per second with the preceding fork. If frequency of tenth fork is four times the frequency of the first fork, calculate the frequency of the first fork.

1. 4 Hz
2. 18 Hz
3. 24 Hz
4. 12 Hz

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. $3$
3. $6$
4. $12$

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

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

Q. Two waves whose equations of displacement of particles in the medium are $y_1=4\sin (500\pi t-25x)$ and $y_2=2\sin (506\pi t-30x)$. How many beats will generate due to the superposition of the two waves and what will be the relation between maximum $\left(I_{max}\right)$ and minimum $\left(I_{min}\right)$ intensity?

1. $3$ beats per second and $I_{max}=2I_{\text{min}}$
2. $3$ beats per second and $I_{max}=9I_{\text{min}}$
3. $6$ beats per second and $I_{max}=2I_{\text{min}}$
4. $6$ beats per second and $I_{max}=9I_{\text{min}}$

Q. Two identical guitar strings of length $L$ are each tuned exactly to $400\text{Hz}$. The tension in one of the strings is then increased by $2\%$. If they are now struck, what is the beat frequency between the fundamental modes of the two strings?

1. $2\text{Hz}$
2. $4\text{Hz}$
3. $6\text{Hz}$
4. $8\text{Hz}$

Q.

A tuning fork gives 4 beats with 50 cm length of a sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is

1. 396

2. 400

3. 404

4. 384

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. 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. A car has source of sound of frequency $256\text{Hz}$ is moving rapidly towards wall with a velocity of $5\text{m/sec}$. How many beats per second will be heard by the driver, if sound travels at a speed of 330 m/sec?

Q. The phenomenon of beats can take place

1. for longitudinal waves only
2. for sound waves only
3. for transverse waves only
4. for both longitudinal and transverse waves

Q. A tuning fork having unknown frequency is sounded together with another tuning fork B of frequency $512H_Z$ 4 beats are heard. Now the tuning fork A is loaded with a little wax. The two forks are again sounded together. Now 5 beats are heard. What is the frequency of A?

1. 506 Hz
2. 507 Hz
3. 508 Hz
4. 509 Hz

Q. When two tuning forks $A$ and $B$ are sounded together, the number of beats heard is $\nu$. The frequency of fork $A$ is $f$. If the prong of fork $B$ is loaded with a little wax, the number of beats decreases. The initial frequency of fork $B$ is

1. $f+\nu$
2. $f-\nu$
3. $f+2\nu$
4. $f-2\nu$