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.