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4

WAVES

One shot

Types

waves

Mechanical Electromagnetic

Mechanical waves

1. Transverse

Mechanical waves

2. longitudinal

Wave characteristics 1. Wavelength ( λ ) : distance between identical points on

consecutive waves.2. Amplitude( A) : distance between origin and crest or trough3. Frequency ( f or 𝜈 ) : number of waves that pass a point per unit

time

Equation of SHW

If the particles of a medium execute SHM, then it's called SHW or plane progressive wave

VELOCITY OF TRANSVERSE WAVE IN STRETCHED STRING

VELOCITY OF SOUND WAVE

INTERFERENCE OF WAVES

INTERFERENCE OF WAVES

INTERFERENCE OF WAVES

BEATS

When two sound waves of slightly different frequencies, travelling along the same direction, superimpose on each other, the intensity of the resultant sound at a particular point rises and falls regularly with time. This is called beats

STATIONARY WAVE

Node N N N N NAntinode AN AN AN AN AN

STANDING WAVES ON STRING FIXED AT BOTH ENDS

Fundamental mode

First overtone

Second overtone

Standing waves on string fixed a one end

AN

N

Standing waves on string fixed a one end

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Standing waves in sound (Closed organ pipe)

1st harmonic = fundamental mode

3rd harmonic/ 1st overtone

5th harmonic/ 2nd overtone

Standing waves in sound (open organ pipe)

1st harmonic = fundamental mode

2nd harmonic/ 1st overtone

3rd harmonic/ 2nd overtone

Doppler effect Standing waves in sound (Closed organ pipe)

Doppler effect Standing waves in sound (Closed organ pipe)

PROBLEMS

Equation of a progressive wave is given by

m. Then which of the

following correct

B

A

λ = 18 m

v = 5 m / sec

D

C a = 0.04 m

n = 50 Hz

Equation of SHW

The equation of a wave travelling on a string is

If x and y are in cm, then

velocity of wave is

B

A

32 cm / sec in - x direction

64 cm / sec in - x direction

D

C 32 cm / sec in + x direction

64 cm / sec in + x direction

Equation of SHW

The equation of a travelling wave is where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

B

A

3.6 x 10-6

3.6 x 10-11

D

C 3.6 x 10-4

3.6

Equation of SHW

If the density of oxygen is 16 times that of hydrogen, what will be the ratio of their corresponding velocities of sound waves at NTP.

B

A

4 : 1

1 : 4

D

C 16 : 1

1 : 16

Velocity of wave

Velocity of sound measured in hydrogen and oxygen gas at a given temperature will be in the ratio

B

A

4 : 1

1 : 4

D

C 2 : 1

1 : 1

Velocity of wave

A string is producing transverse vibration whose equation is y = 0.021 sin (x + 30t), Where x and y are in meters and t is in seconds. If the linear density of the string is 1.3 x 10-4 kg/m, then the tension in the string in N will be

B

A

0.5

10

D

C 1

0.117

Velocity of wave

A string in musical instrument is 50 cm long and its fundamental frequency is 800 Hz. If a frequency of 1000 Hz is to be produced, then required length of string is

B

A

50 cm

62.5 cm

D

C 40 cm

37.5 cm

Stationary waves on string

Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is

B

A

4 Hz

2 Hz

D

C 5 Hz

10 Hz

Stationary waves on string

Two uniform strings A and B made of steel are made to vibrate under the same tension. If the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is

B

A

1 : 3

1 : 2

D

C 1 : 4

1 : 6

Stationary waves on string

A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio

B

A

2 : 3

1 : 2

D

C 3 : 4

4 : 5

Organ pipe

Two closed organ pipes, when sounded simultaneously gave 4 beats per sec. If longer pipe has a length of 1m. Then length of shorter pipe will be, (v = 300 m/s)

B

A

94.9 cm

185.g cm

D

C 90 cm

80 cm

Organ pipe

A closed organ pipe is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is

B

A

4 : 1

1 : 2

D

C 8 : 3

3 : 8

Organ pipe

The wavelength is 120 cm when the source is stationary. If the source is moving with relative velocity of 60 m/sec towards the observer, then the wavelength of the sound wave reaching to the observer will be (velocity of sound = 330 m/s)

B

A

140 cm

98 cm

D

C 120 cm

144 cm

Doppler effect

A source of sound is moving with constant velocity of 20 m/s emitting a note of frequency 1000 Hz. The ratio of frequencies observed by a stationary observer while the source is approaching him and after it crosses him will be (Speed of sound v = 340 m/s)

B

A

8 : 9

9 : 8

D

C 1 : 1

9 : 10

Doppler effect

A source of sound S of frequency 500 Hz situated between a stationary observer O and a wall W, moves towards the wall with a speed of 2 m/s. If the velocity of sound is 332 m/s, then the number of beats per second heard by the observer is (approximately)

B

A

6

8

D

C 4

2

Doppler effect

How to cover missed topics??

How to coverMissed Topics?

JEE MAIN 2021 CRASH COURSE Course Overview

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