In the figure at the right is shown three graphs of the shapes of the same taut
ID: 1475434 • Letter: I
Question
In the figure at the right is shown three graphs of the shapes of the same taut elastic string in three different circumstances, labelled A, B, and C. In some of the problems below, the string represents a guitar string, tied down at both ends, while in others, it is part of a very long telephone wire whose ends are not shown. Be careful to note which is which for each problem! The string is light enough that the effects of gravity can be ignored. In each case, the bit of string at the position x = 23 cm is painted blue.
1. Suppose the three graphs all represent the same string, tied down at x = 0 and x = 70 cm, and at the same tension. What can you say about the three frequencies of oscillation?
A. Situation A has the highest frequency.
B. Situation C has the highest frequency.
C. You cant say anything from the information given.
D. The three frequencies are all the same.
E. Situation B has the highest frequency.
2. Suppose the three graphs all represent the same string, tied down at x = 0 and x = 70 cm, but their tensions have been adjusted so that all three situations are all oscillating at the same frequency. What can you say about the tensions in the three cases?
A. The tension is string A is the greatest.
B. You cant adjust the tensions to make the frequencies the same since the wavelengths are different.
C. The tension in string C is the greatest.
D. All three tensions are the same.
E. You cant say anything from the information given.
3. Suppose that graph C represents the string, tied down at x = 0 and x = 70 cm, under tension. What can you say about the acceleration of the blue bead in case C at the instant shown?
A. It is upward.
B. It is 0.
C. It is downward.
D. You cant say anything from the information given.
4. Suppose that graph C represents part of a long wire, under tension, and is showing a left traveling wave at a particular instant. What can you say about the velocity of the blue bead in case C at the instant shown?
A. It is downward.
B. You cant say anything from the information given.
C. It is 0.
D. It is upward.
5. Suppose that graph C represents part of a long wire, under tension, and is showing a left traveling wave at a particular instant. What can you say about the acceleration of the blue bead in case C at the instant shown?
A. It is downward.
B. You cant say anything from the information given.
C. It is 0.
D. It is upward.
In the figure at the right is shown three graphs of the shapes of the same taut elastic string in three different circumstances, labelled A, B, and C. In some of the problems below, the string represents a guitar string, tied down at both ends, while in others, it is part of a very long telephone wire whose ends are not shown. Be careful to note which is which for each problem! The string is light enough that the effects of gravity can be ignored. In each case, the bit of string at the position x = 23 cm is painted blue.
1. Suppose the three graphs all represent the same string, tied down at x = 0 and x = 70 cm, and at the same tension. What can you say about the three frequencies of oscillation?
A. Situation A has the highest frequency.
B. Situation C has the highest frequency.
C. You cant say anything from the information given.
D. The three frequencies are all the same.
E. Situation B has the highest frequency.
Explanation / Answer
speed of a standing wave on a string is given by
v=sqrt(tension/mass per unit length)
as strings are indental, mass per unit length is constant for all three strings
as tension is constant, they all have same speed.
now, as we know wavelength*frequency=speed of a wave
as speed is constant, frequency is inversely proportional to wavelength
wavelength is the distance between consecutive peaks or consecutives crests.
hence smaller the wavelength, larger the frequency.
hence for string C frequency is the highest as the wavelength is smaller.
hence option B is correct.
part 2:
as frequency*wavelength=speed
here frequency is kept constant, then speed is directly proportional to the wavelength
as speed=sqrt(tension/mass per unit length)
tension is proportional to square of wavelength.
hence larger the wavelength, larger the tension.
hence tension in string A is the greatest as wavelength is largest.
option A is correct.
part 3:
blue bead is at equilibrium position
hence acceleration is 0.
part 4:
equation of travelling wave:
y(x,t)=A*sin(w*t-k*x)
veloicty=partial derivative of y w.r.t. t
=A*w*cos(w*t-k*x)
as y(x,t)=0 for the blue bead,
sin(w*t-k*x)=0
hence cos(w*t-k*x)=1
then y(x,t)=A*w
which is positive
hence the velocity is upward direction