1. A string having a mass
per unit length of 10.0 g/m is under a tension of 160 N. This string resonates
in the mode shown in figure 1. If the length of this string is 90.0 cm, find
the frequency of oscillation.
211 Hz
2. The equation for a
transverse wave on a string is:
y(x,t) = 10.0*sin(0.157*x - 50.3*t)
where x and y are in centimeters and t is in seconds.
At a given time, how far
apart are two points that differ in phase by Pi/2 radians?
10.0 cm
3. The wave function for a
standing wave on a string is:
y(x,t) = 2.0*sin(0.25*Pi*x)*cos(120*Pi*t)
where x and y are in centimeters and t is in seconds.
What is the distance
between two adjacent nodes?
4.0 cm
4. Two sinusoidal waves
having the same amplitude (A), frequency and wavelength, travel in the same
direction and have a phase difference Phi.
Which one of the following
statements is TRUE?
A: Their interference will
be constructive if Phi = 100 Pi.
B: Their interference will
be constructive if Phi = Pi.
C: The resultant wave will
be a standing wave for Phi = 0.
D: For certain values of
Phi, the amplitude of the resultant reaches 4A.
E: The frequency of the
resultant wave is twice the original frequency.
5. The linear density of a vibrating string is 1 g/m. A transverse
wave is propagating on the string and is given by the equation:
y(x,t) = 2.0*sin(x -
40*t),
where x and y are in meters and t is in
seconds.
What is the tension in the string?
1.6 N.
6. Which of the following statements are CORRECT:
1. Waves carry energy and momentum.
2. Mechanical waves need a medium to
propagate.
3. Sound waves are transverse waves.
4. A Wave on a stretched string is a
longitudinal wave.
5. For a tube closed at one end, only odd
harmonics are present.
A 1, 2, and 5.
B 2 and 4.
C 1, 2 and 3.
D 1 and 4.
E 3 and 5.