Solved Example: Oscillation and Waves | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Example on Oscillation and Waves 
JEE Mains 
Q1: A firecracker exploding on the surface of lake is heard as two sounds at a time interval ?? apart 
by a man on a boat close to water surface. Sound travels with a speed ?? in water and a speed ?? in 
air. The distance from the exploding firecracker to the boat is 
(A) 
?????? ?? +?? 
(B) 
?? (?? +?? )
????
 
(C) 
?? (?? -?? )
????
 
(D) 
?????? ?? -?? 
 Ans: (D) ?? = ?? ?? 0
 ? ?? = ?? (?? 0
+ ?? )
 ? (?? - ?? )?? 0
+ ???? = 0
?? 0
=
????
?? - ?? ?? =
?????? ?? - ?? 
 
 
Q2:  A sonometer wire has a total length of ?? ?? between the fixed ends. Two wooden bridges are 
placed below the wire at a distance ?? /?? ?? from one end and ?? /?? ?? from the other end. The 
three segments of the wire have their fundamental frequencies in the ratio: 
(A) ?? : ?? : ?? 
(B) ?? : ?? : ?? 
(C) ?? : ?? /?? : ?? /?? 
(D) 1:1:1 
Ans: (B) 
 
l =
7?? 2
?? =
2l
7
?? ratio : 1: 2: 4
?? ratio : 4: 2: 1
 
Page 2


JEE Solved Example on Oscillation and Waves 
JEE Mains 
Q1: A firecracker exploding on the surface of lake is heard as two sounds at a time interval ?? apart 
by a man on a boat close to water surface. Sound travels with a speed ?? in water and a speed ?? in 
air. The distance from the exploding firecracker to the boat is 
(A) 
?????? ?? +?? 
(B) 
?? (?? +?? )
????
 
(C) 
?? (?? -?? )
????
 
(D) 
?????? ?? -?? 
 Ans: (D) ?? = ?? ?? 0
 ? ?? = ?? (?? 0
+ ?? )
 ? (?? - ?? )?? 0
+ ???? = 0
?? 0
=
????
?? - ?? ?? =
?????? ?? - ?? 
 
 
Q2:  A sonometer wire has a total length of ?? ?? between the fixed ends. Two wooden bridges are 
placed below the wire at a distance ?? /?? ?? from one end and ?? /?? ?? from the other end. The 
three segments of the wire have their fundamental frequencies in the ratio: 
(A) ?? : ?? : ?? 
(B) ?? : ?? : ?? 
(C) ?? : ?? /?? : ?? /?? 
(D) 1:1:1 
Ans: (B) 
 
l =
7?? 2
?? =
2l
7
?? ratio : 1: 2: 4
?? ratio : 4: 2: 1
 
 
 
Q3:  A person can hear frequencies only up to ?????????? . A steel piano wire ???? ???? long of mass ?? ?? is 
stretched with a tension of ?????? ?? . The number of the highest overtone of the sound produced by 
this piano wire that the person can hear is 
(A) 4 
(B) 50 
(C) 49 
(D) 51 
Ans: (C) ?? =
5×10
-3
0.5
= 0.01 
?? = 400 N
?? =
(?? + 1)
2 × 0.5
v
400
0.01
?? = 200 (?? + 1) < 10
4
 ? (?? + 1) < 50
 ? ?? < 49
 
 
Q4:  How many times intense is ???? ???? sound than ???? ???? sound? 
(A) 5 
(B) 50 
(C) 500 
(D) ????
?? 
Ans:  (D) 10log (
?? 2
?? 1
) = 50 
?? 2
= ?? 1
× 10
5
 
 
Q5:  At a prayer meeting, the disciples sing jai -ram jairam. The sound amplified by a loudspeaker 
comes back after reflection from a builder at a distance of ???? ?? from the meeting. What 
maximum time interval can be kept between one jai -ram and the next jai-ram so that the echo 
does not disturb a listener sitting in the meeting? Speed of sound in air is ?????? ????
-?? . 
(A) 20 Seconds 
(B) 0.3 Seconds 
(C) 40 Seconds 
(D) 0.5 Seconds 
Ans:  (D) Here given ?? = 80 m × 2 = 160 m. 
V = 320 m/s 
So the maximum time interval will be ?? = 5/?? = 160/320 = 0.5 seconds. 
 
Page 3


JEE Solved Example on Oscillation and Waves 
JEE Mains 
Q1: A firecracker exploding on the surface of lake is heard as two sounds at a time interval ?? apart 
by a man on a boat close to water surface. Sound travels with a speed ?? in water and a speed ?? in 
air. The distance from the exploding firecracker to the boat is 
(A) 
?????? ?? +?? 
(B) 
?? (?? +?? )
????
 
(C) 
?? (?? -?? )
????
 
(D) 
?????? ?? -?? 
 Ans: (D) ?? = ?? ?? 0
 ? ?? = ?? (?? 0
+ ?? )
 ? (?? - ?? )?? 0
+ ???? = 0
?? 0
=
????
?? - ?? ?? =
?????? ?? - ?? 
 
 
Q2:  A sonometer wire has a total length of ?? ?? between the fixed ends. Two wooden bridges are 
placed below the wire at a distance ?? /?? ?? from one end and ?? /?? ?? from the other end. The 
three segments of the wire have their fundamental frequencies in the ratio: 
(A) ?? : ?? : ?? 
(B) ?? : ?? : ?? 
(C) ?? : ?? /?? : ?? /?? 
(D) 1:1:1 
Ans: (B) 
 
l =
7?? 2
?? =
2l
7
?? ratio : 1: 2: 4
?? ratio : 4: 2: 1
 
 
 
Q3:  A person can hear frequencies only up to ?????????? . A steel piano wire ???? ???? long of mass ?? ?? is 
stretched with a tension of ?????? ?? . The number of the highest overtone of the sound produced by 
this piano wire that the person can hear is 
(A) 4 
(B) 50 
(C) 49 
(D) 51 
Ans: (C) ?? =
5×10
-3
0.5
= 0.01 
?? = 400 N
?? =
(?? + 1)
2 × 0.5
v
400
0.01
?? = 200 (?? + 1) < 10
4
 ? (?? + 1) < 50
 ? ?? < 49
 
 
Q4:  How many times intense is ???? ???? sound than ???? ???? sound? 
(A) 5 
(B) 50 
(C) 500 
(D) ????
?? 
Ans:  (D) 10log (
?? 2
?? 1
) = 50 
?? 2
= ?? 1
× 10
5
 
 
Q5:  At a prayer meeting, the disciples sing jai -ram jairam. The sound amplified by a loudspeaker 
comes back after reflection from a builder at a distance of ???? ?? from the meeting. What 
maximum time interval can be kept between one jai -ram and the next jai-ram so that the echo 
does not disturb a listener sitting in the meeting? Speed of sound in air is ?????? ????
-?? . 
(A) 20 Seconds 
(B) 0.3 Seconds 
(C) 40 Seconds 
(D) 0.5 Seconds 
Ans:  (D) Here given ?? = 80 m × 2 = 160 m. 
V = 320 m/s 
So the maximum time interval will be ?? = 5/?? = 160/320 = 0.5 seconds. 
 
 
 
 
Q6:  A man stands before a large wall at a distance of ???? . ?? ?? and claps his hands at regular 
intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value 
when the echo of a clap merges with the next clap 10 times during every 3 seconds. Find the 
velocity of sound in air. 
(A) ?????? ?? /?? 
(B) ?????? ?? /?? 
(C) ?????? ?? /?? 
(D) ?????? ?? /?? 
Ans: (B) He has to clap 10 times in 3 seconds. 
So time interval between two clap = (3/10 second ). 
So the time taken go the wall 
= (3/2 × 10) = 3/20 seconds = 333 m/s.  
 
 
Q7:  Find the minimum and maximum wavelength of sound in water that is in the audible range 
(???? - ?????????? ???? ) for an average human ear. Speed of sound in water = ???????? ???? . 
(A) ???? . ?? ?? 
(B) ???? . ?? ?? 
(C) ???? . ?? ?? 
(D) ???? . ?? ?? 
Ans: (A) For minimum wavelength ?? = 20KHZ 
? ?? = ???? ? ?? = (
1450
20 × 10
3
) = 7.25 cm.  
(b) For maximum wavelength ?? should be minimum 
? ?? = ???? ? ?? = ?? /?? ? 1450 /20 = 72.5?? .  
 
 
 
 
 
 
Page 4


JEE Solved Example on Oscillation and Waves 
JEE Mains 
Q1: A firecracker exploding on the surface of lake is heard as two sounds at a time interval ?? apart 
by a man on a boat close to water surface. Sound travels with a speed ?? in water and a speed ?? in 
air. The distance from the exploding firecracker to the boat is 
(A) 
?????? ?? +?? 
(B) 
?? (?? +?? )
????
 
(C) 
?? (?? -?? )
????
 
(D) 
?????? ?? -?? 
 Ans: (D) ?? = ?? ?? 0
 ? ?? = ?? (?? 0
+ ?? )
 ? (?? - ?? )?? 0
+ ???? = 0
?? 0
=
????
?? - ?? ?? =
?????? ?? - ?? 
 
 
Q2:  A sonometer wire has a total length of ?? ?? between the fixed ends. Two wooden bridges are 
placed below the wire at a distance ?? /?? ?? from one end and ?? /?? ?? from the other end. The 
three segments of the wire have their fundamental frequencies in the ratio: 
(A) ?? : ?? : ?? 
(B) ?? : ?? : ?? 
(C) ?? : ?? /?? : ?? /?? 
(D) 1:1:1 
Ans: (B) 
 
l =
7?? 2
?? =
2l
7
?? ratio : 1: 2: 4
?? ratio : 4: 2: 1
 
 
 
Q3:  A person can hear frequencies only up to ?????????? . A steel piano wire ???? ???? long of mass ?? ?? is 
stretched with a tension of ?????? ?? . The number of the highest overtone of the sound produced by 
this piano wire that the person can hear is 
(A) 4 
(B) 50 
(C) 49 
(D) 51 
Ans: (C) ?? =
5×10
-3
0.5
= 0.01 
?? = 400 N
?? =
(?? + 1)
2 × 0.5
v
400
0.01
?? = 200 (?? + 1) < 10
4
 ? (?? + 1) < 50
 ? ?? < 49
 
 
Q4:  How many times intense is ???? ???? sound than ???? ???? sound? 
(A) 5 
(B) 50 
(C) 500 
(D) ????
?? 
Ans:  (D) 10log (
?? 2
?? 1
) = 50 
?? 2
= ?? 1
× 10
5
 
 
Q5:  At a prayer meeting, the disciples sing jai -ram jairam. The sound amplified by a loudspeaker 
comes back after reflection from a builder at a distance of ???? ?? from the meeting. What 
maximum time interval can be kept between one jai -ram and the next jai-ram so that the echo 
does not disturb a listener sitting in the meeting? Speed of sound in air is ?????? ????
-?? . 
(A) 20 Seconds 
(B) 0.3 Seconds 
(C) 40 Seconds 
(D) 0.5 Seconds 
Ans:  (D) Here given ?? = 80 m × 2 = 160 m. 
V = 320 m/s 
So the maximum time interval will be ?? = 5/?? = 160/320 = 0.5 seconds. 
 
 
 
 
Q6:  A man stands before a large wall at a distance of ???? . ?? ?? and claps his hands at regular 
intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value 
when the echo of a clap merges with the next clap 10 times during every 3 seconds. Find the 
velocity of sound in air. 
(A) ?????? ?? /?? 
(B) ?????? ?? /?? 
(C) ?????? ?? /?? 
(D) ?????? ?? /?? 
Ans: (B) He has to clap 10 times in 3 seconds. 
So time interval between two clap = (3/10 second ). 
So the time taken go the wall 
= (3/2 × 10) = 3/20 seconds = 333 m/s.  
 
 
Q7:  Find the minimum and maximum wavelength of sound in water that is in the audible range 
(???? - ?????????? ???? ) for an average human ear. Speed of sound in water = ???????? ???? . 
(A) ???? . ?? ?? 
(B) ???? . ?? ?? 
(C) ???? . ?? ?? 
(D) ???? . ?? ?? 
Ans: (A) For minimum wavelength ?? = 20KHZ 
? ?? = ???? ? ?? = (
1450
20 × 10
3
) = 7.25 cm.  
(b) For maximum wavelength ?? should be minimum 
? ?? = ???? ? ?? = ?? /?? ? 1450 /20 = 72.5?? .  
 
 
 
 
 
 
Q8:  The sound level at a point ?? . ?? ?? away from a point source is ???? ???? . What will be the level at 
a point ???? ?? away from the source? 
(A) ???????? 
(B) ?????? 
(C) ???????? 
(D) ???????? 
Ans: (C) Weknow that ?? = 10log
10
 (
I
I
0
) 
?? ?? = 10log 
?? ?? ?? 0
, ?? ?? = 10log 
?? ?? ?? 0
 ? ?? ?? /?? 0
= 10
(?? ?? /10)
? ?? ?? /?? 0
= 10
(?? ?? /10)
 ?
?? ?? ?? ?? =
?? ?? 2
?? ?? 2
= (
50
5
)
2
? 10
(?? ?? ?? ?? )=10
2
 ?
?? ?? - ?? ?? 10
= 2 ? ?? ?? = 40 - 20 = 20 d?? 
 
 
Q9:  A source of sound ?? and a detector ?? are placed at some distance from one another. A big 
cardboard is placed near the detector and perpendicular to the line SD as shown in figure. It is 
gradually moved away and it is shown that the intensity change from a maximum to a minimum as 
the board is moved through a distance of ???? ???? . What will be the frequency of the sound emitted. 
Velocity of sound in air is ?????? ????
 
. 
 
(A) ?????? ???? 
(B) ?????? ???? 
(C) ?????? ???? 
(D) ?????? ???? 
Ans:  (A) According to the given data 
?? = 336 m/s,  
?? /4 = distance between maximum and minimum intensity 
 = (20 cm) ? ?? = 80 cm
 ? n = frequency =
V
?? =
336
80 × 10
-2
= 420 Hz.
 
Page 5


JEE Solved Example on Oscillation and Waves 
JEE Mains 
Q1: A firecracker exploding on the surface of lake is heard as two sounds at a time interval ?? apart 
by a man on a boat close to water surface. Sound travels with a speed ?? in water and a speed ?? in 
air. The distance from the exploding firecracker to the boat is 
(A) 
?????? ?? +?? 
(B) 
?? (?? +?? )
????
 
(C) 
?? (?? -?? )
????
 
(D) 
?????? ?? -?? 
 Ans: (D) ?? = ?? ?? 0
 ? ?? = ?? (?? 0
+ ?? )
 ? (?? - ?? )?? 0
+ ???? = 0
?? 0
=
????
?? - ?? ?? =
?????? ?? - ?? 
 
 
Q2:  A sonometer wire has a total length of ?? ?? between the fixed ends. Two wooden bridges are 
placed below the wire at a distance ?? /?? ?? from one end and ?? /?? ?? from the other end. The 
three segments of the wire have their fundamental frequencies in the ratio: 
(A) ?? : ?? : ?? 
(B) ?? : ?? : ?? 
(C) ?? : ?? /?? : ?? /?? 
(D) 1:1:1 
Ans: (B) 
 
l =
7?? 2
?? =
2l
7
?? ratio : 1: 2: 4
?? ratio : 4: 2: 1
 
 
 
Q3:  A person can hear frequencies only up to ?????????? . A steel piano wire ???? ???? long of mass ?? ?? is 
stretched with a tension of ?????? ?? . The number of the highest overtone of the sound produced by 
this piano wire that the person can hear is 
(A) 4 
(B) 50 
(C) 49 
(D) 51 
Ans: (C) ?? =
5×10
-3
0.5
= 0.01 
?? = 400 N
?? =
(?? + 1)
2 × 0.5
v
400
0.01
?? = 200 (?? + 1) < 10
4
 ? (?? + 1) < 50
 ? ?? < 49
 
 
Q4:  How many times intense is ???? ???? sound than ???? ???? sound? 
(A) 5 
(B) 50 
(C) 500 
(D) ????
?? 
Ans:  (D) 10log (
?? 2
?? 1
) = 50 
?? 2
= ?? 1
× 10
5
 
 
Q5:  At a prayer meeting, the disciples sing jai -ram jairam. The sound amplified by a loudspeaker 
comes back after reflection from a builder at a distance of ???? ?? from the meeting. What 
maximum time interval can be kept between one jai -ram and the next jai-ram so that the echo 
does not disturb a listener sitting in the meeting? Speed of sound in air is ?????? ????
-?? . 
(A) 20 Seconds 
(B) 0.3 Seconds 
(C) 40 Seconds 
(D) 0.5 Seconds 
Ans:  (D) Here given ?? = 80 m × 2 = 160 m. 
V = 320 m/s 
So the maximum time interval will be ?? = 5/?? = 160/320 = 0.5 seconds. 
 
 
 
 
Q6:  A man stands before a large wall at a distance of ???? . ?? ?? and claps his hands at regular 
intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value 
when the echo of a clap merges with the next clap 10 times during every 3 seconds. Find the 
velocity of sound in air. 
(A) ?????? ?? /?? 
(B) ?????? ?? /?? 
(C) ?????? ?? /?? 
(D) ?????? ?? /?? 
Ans: (B) He has to clap 10 times in 3 seconds. 
So time interval between two clap = (3/10 second ). 
So the time taken go the wall 
= (3/2 × 10) = 3/20 seconds = 333 m/s.  
 
 
Q7:  Find the minimum and maximum wavelength of sound in water that is in the audible range 
(???? - ?????????? ???? ) for an average human ear. Speed of sound in water = ???????? ???? . 
(A) ???? . ?? ?? 
(B) ???? . ?? ?? 
(C) ???? . ?? ?? 
(D) ???? . ?? ?? 
Ans: (A) For minimum wavelength ?? = 20KHZ 
? ?? = ???? ? ?? = (
1450
20 × 10
3
) = 7.25 cm.  
(b) For maximum wavelength ?? should be minimum 
? ?? = ???? ? ?? = ?? /?? ? 1450 /20 = 72.5?? .  
 
 
 
 
 
 
Q8:  The sound level at a point ?? . ?? ?? away from a point source is ???? ???? . What will be the level at 
a point ???? ?? away from the source? 
(A) ???????? 
(B) ?????? 
(C) ???????? 
(D) ???????? 
Ans: (C) Weknow that ?? = 10log
10
 (
I
I
0
) 
?? ?? = 10log 
?? ?? ?? 0
, ?? ?? = 10log 
?? ?? ?? 0
 ? ?? ?? /?? 0
= 10
(?? ?? /10)
? ?? ?? /?? 0
= 10
(?? ?? /10)
 ?
?? ?? ?? ?? =
?? ?? 2
?? ?? 2
= (
50
5
)
2
? 10
(?? ?? ?? ?? )=10
2
 ?
?? ?? - ?? ?? 10
= 2 ? ?? ?? = 40 - 20 = 20 d?? 
 
 
Q9:  A source of sound ?? and a detector ?? are placed at some distance from one another. A big 
cardboard is placed near the detector and perpendicular to the line SD as shown in figure. It is 
gradually moved away and it is shown that the intensity change from a maximum to a minimum as 
the board is moved through a distance of ???? ???? . What will be the frequency of the sound emitted. 
Velocity of sound in air is ?????? ????
 
. 
 
(A) ?????? ???? 
(B) ?????? ???? 
(C) ?????? ???? 
(D) ?????? ???? 
Ans:  (A) According to the given data 
?? = 336 m/s,  
?? /4 = distance between maximum and minimum intensity 
 = (20 cm) ? ?? = 80 cm
 ? n = frequency =
V
?? =
336
80 × 10
-2
= 420 Hz.
 
 
 
 
Q10:  Two sources of sound, ?? ?? and ?? ?? , emitting waves of equal wavelength ???? . ?? ???? , are placed 
with a separation of ???? . ?? ???? between them. A detector can be moved on a line parallel to ?? ?? ?? ?? 
and at a distance of ???? . ?? ???? from it. Initially, the detector is equidistant from the two sources. 
Assuming that the waves emitted by the sources are in phase, find the minimum distance through 
which the detector should be shifted to detect a minimum frequency of sound. 
(A) ???? ???? 
(B) ???? ???? 
(C) ???? ???? 
(D) ???? ???? 
Ans: (A) According to the data 
?? = 20 cm, S
1
 S
2
= 20 cm, BD = 20 cm 
Let the detector is shifted to left for a distance x for hearing the minimum sound. 
So path difference ???? = ???? - ???? 
= v(20)
2
+ (10 + ?? )
2
- v(20)
2
+ (10 - ?? )
2
 
So the minimum distances hearing for minimum 
 =
(2?? + 1)?? 2
=
?? 2
=
20
2
= 10 cm
 ? v(20)
2
+ (10 + ?? )
2
- v(20)
2
+ (10 - ?? )
2
= 10
 
Solving we get ?? = 12.0 cm. 
 
 
Q11:  A cylindrical metal tube has a length of ???? ???? and is open at both ends. Find the frequencies 
between ???????? ???? and ???????? ???? at which the air column in the tube can resonate. Speed of sound 
in air is ?????? ????
?? . 
(A) ???????? ???? , ???????? ???? , ???????? ???? 
(B) ???????? ???? , ???????? ???? , ???????? ???? 
(C) ???????? ???? , ???????? ???? , ???????? ???? 
(D) ???????? ???? , ???????? ???? , ???????? ????