Q14.Wave Motion

Q14. Wave Motion

1. The displacement of a string carrying a traveling sinusoidal

wave is given by

1. v0 /y0

2. y0 / v0

3. v0 / y0

4. y0 / v0

5. v0 y0

, sinmy x t y k x t

At time t 0 the point at x 0 has velocity v0 and

displacement y0. The phase constant is given by tan :

0 sinmy y

0 cosmv y

0

0

tany

v

, sinmy x t y k x t

, cosmv x t y k x t

1. The displacement of a string carrying a traveling sinusoidal wave is given by

, sinmy x t y k x t

At time t 0 the point at x 0 has velocity v0 and displacement y0.

The phase constant is given by tan :

2. The diagram shows three identical strings that have been put

under tension by suspending masses of 5 kg each. For

which is the wave speed the greatest ?

1. 1

2. 2

3. 3

4. 1 and 3 tie

5. 2 and 3 tie

Tv

Larger T larger v

T Mg 1

2T Mg T Mg

Ans: 1 & 3 tied

3. The tension in a string with a linear density of 0.0010 kg/m is

0.40 N. A 100 Hz sinusoidal wave on this string has a

wavelength of :

1. 0.05 cm

2. 2.0 cm

3. 5.0 cm

4. 20 cm

5. 500 cm

Tv

1v T

f f

0.401

0.2 20100 0.0010 /

Nm cm

Hz kg m

3. The tension in a string with a linear density of 0.0010 kg/m is

0.40 N. A 100 Hz sinusoidal wave on this string has a

wavelength of :

4. Suppose the maximum speed of a string carrying a sinusoidal

wave is vs. When the displacement of a point on the string

is half its maximum, the speed of the point is :

1. vs / 2

2. 2 vs

3. vs / 4

4. 3 vs / 4

5. 3 vs / 2

sinmy y k x t cosmv y k x t

s mv y

1

2 my y 1sin

2k x t

2

1 3cos 1

2 2k x t

3 3

2 2m sv y v

4. Suppose the maximum speed of a string carrying a sinusoidal wave is vs.

When the displacement of a point on the string is half its maximum, the

speed of the point is :

5. Two sinusoidal waves have the same angular frequency, the

same amplitude ym, and travel in the same direction in the

same medium. If they differ in phase by 50°, the amplitude

of the resultant wave is given by :

1. 0.64 ym

2. 1.3 ym

3. 0.91 ym

4. 1.8 ym

5. 0.35 ym

1

2

sin

sinm

m

y y

y y

Amplitude

50

180

1 2 sin sinmy y y 2 sin cos2 2my

k x t

2 cos 1.812m my y

5. Two sinusoidal waves have the same angular frequency, the

same amplitude ym, and travel in the same direction in the

same medium. If they differ in phase by 50°, the amplitude

of the resultant wave is given by :

6. The sinusoidal wave y(x,t) ym sin( k x – t ) is incident

on the fixed end of a string at x L. The reflected wave is

given by :

1. ym sin( k x + t )

2. –ym sin( k x + t )

3. ym sin( k x + t – k

L )

4. ym sin( k x + t – 2

k L )

5. –ym sin( k x + t + 2

k L )

0, sinrefl my x t y k x L t t

Let the time of incidence be t0

0 0 0, sin 0 ,in m refly L t y k L t y L t

0sinmy k x t k L t

sin 2my k x t k L

0k L t

6. The sinusoidal wave y(x,t) ym sin( k x – t ) is incident

on the fixed end of a string at x L. The reflected wave is

given by :

7. Standing waves are produced by the interference of two

traveling sinusoidal waves, each of frequency 100 Hz. The

distance from the 2nd node to the 5th node is 60 cm. The

wavelength of each of the two original waves is :

1. 50 cm

2. 40 cm

3. 30 cm

4. 20 cm

5. 15 cm

1 siny A k x t

In order to have a standing wave, these waves must travel in opposite directions.

2 siny A k x t

1 2 sin cos2 2

y y A t k x

Distance from the 2nd node to the 5th node is 60 cm :

260 5 2cm

40 cm

7. Standing waves are produced by the interference of two traveling sinusoidal

waves, each of frequency 100 Hz. The distance from the 2nd node to the

5th node is 60 cm. The wavelength of each of the two original waves is :

8. A stretched string, clamped at its ends, vibrates in its

fundamental frequency. To double the fundamental

frequency, one can change the string tension by a factor of :

1. 2

2. 4

3. 2

4. 1 /

2

5. 1 /

2

2T v

Clamped at ends & fundamental mode fixed

v fk

2T f

2 4f f T T

8. A stretched string, clamped at its ends, vibrates in its

fundamental frequency. To double the fundamental

frequency, one can change the string tension by a factor of :

9. A 40-cm long string, with one end clamped and the other free

to move transversely, is vibrating in its fundamental standing

wave mode. If the wave speed is 320 cm/s, the frequency is

:

1. 32

Hz

2. 16

Hz

3. 8

Hz

4. 4

Hz

5. 2

Hz

320 /

24 40

cm svf Hz

cm

One end clamped and the other free to move transversely.

Fundamental standing wave mode 4 L.

9. A 40-cm long string, with one end clamped and the other free

to move transversely, is vibrating in its fundamental standing

wave mode. If the wave speed is 320 cm/s, the frequency is

: