Transcript Q05. Using Newtons Laws - National Cheng Kung University

Q14. Wave Motion
1. The displacement of a string carrying a traveling sinusoidal
y  x, t   ym sin  k x  wt   
wave is given by
At time t  0 the point at x  0 has velocity v0 and displacement
y0 .
The phase constant  is given by tan   :
1.
v0 / w y0
2.
w y0 / v0
3.
w v0 / y0
4.
y0 / w v0
5.
w v0 y0
1.
The displacement of a string carrying a traveling sinusoidal wave is given by
y  x, t   ym sin  k x  wt   
At time t  0 the point at x  0 has velocity v0 and displacement y0.
The phase constant  is given by tan   :
y  x, t   ym sin  k x  wt   
y0   ym sin 
v  x, t   w ym cos  k x  wt   
v0  w ym cos
tan  
w y0
v0
2. The diagram shows three identical strings that have been put
under tension by suspending masses of 5 kg each.
which is the wave speed the greatest ?
1.
1
2.
2
3.
3
4.
1 and 3 tie
5.
2 and 3 tie
For
v
T
T  Mg

 Larger T
1
T  Mg
2
Ans: 1 & 3 tied
 larger v
T  Mg
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
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 :
v
T

v 1
 
f
f
1

100 Hz 
T

 0.40 N 
 0.0010 kg / m 
 0.2 m  20 cm
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
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 :
y  ym sin  k x  w t   

y
1
ym
2
v  w ym cos  k x  w t   
vs  w ym

1
 sin  k x  w t   
2
cos  k x  w t    
v  w ym
2
3
1
1   
2
2
3
3

vs
2
2
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
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 :
y1  ym sin 
  k x w t
y2  ym sin     
50


180
 

y1  y2  ym sin   sin        2 ym sin     cos
2
2

 Amplitude  2 ym cos

2
 1.81 ym
6. The sinusoidal wave
y(x,t)  ym sin( k x – w t ) is incident
on the fixed end of a string at x  L.
The reflected wave is
given by :
1.
ym sin( k x + w t )
2.
–ym sin( k x + w t )
3.
ym sin( k x + w t – k L )
4.
ym sin( k x + w t – 2 k L )
5.
–ym sin( k x + w t + 2 k L )
6. The sinusoidal wave y(x,t)  ym sin( k x – w t ) is incident
on the fixed end of a string at x  L.
The reflected wave is
given by :
Let the time of incidence be t0
yin  L, t0   ym sin  k L  w t0   0  yrefl  L, t0 

k L  w t0
yrefl  x, t   ym sin  k  x  L   w  t  t0    
 ym sin  k x  w t  k L  w t0 
 ym sin  k x  w t  2k L
7. Standing waves are produced by the interference of two
traveling sinusoidal waves, each of frequency 100 Hz.
distance from the 2nd node to the 5th node is 60 cm.
wavelength of each of the two original waves is :
1.
50 cm
2.
40 cm
3.
30 cm
4.
20 cm
5.
15 cm
The
The
7.
Standing waves are produced by the interference of two traveling sinusoidal
waves, each of frequency 100 Hz.
5th node is 60 cm.
The distance from the 2nd node to the
The wavelength of each of the two original waves is :
In order to have a standing wave, these waves must travel in opposite directions.
y1  A sin  k x  w t 
y2  A sin  k x  w t   
 


y1  y2  A sin  w t   cos  k x  
2
2


Distance from the 2nd node to the 5th node is 60 cm :
2

 60 cm    5  2  

  40 cm
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
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 :
T v
v
2
w
k
 f
Clamped at ends & fundamental mode

 fixed

T f2
f 2f

T  4T
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
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 :
One end clamped and the other free to move transversely.
Fundamental standing wave mode
f

  4 L.
320 cm / s 

 
 2 Hz
  4  40 cm
v